take home exercise 2 Singapore public bus commuter flows

Author

Xu Lin

overview

We currently have data on people’s movement patterns as well as information on schools, businesses, and retail activities in different areas. The goal of this task is to identify common Saturday activities among the population. Through our analysis, we aim to provide recommendations to the government, suggesting potential enhancements to existing facilities or proposing the development of new amenities that align with people’s preferences. The objective is to make these facilities more appealing and strategically located for the community’s convenience.

Objective

Our goal is to pinpoint popular weekend destinations, analyze the main facilities in those areas, and provide recommendations accordingly.

Data Geospatial data:

Passenger Volume by Origin Destination Bus Stops, Bus Stop Location, Train Station and Train Station Exit Point, Master Plan 2019 Subzone Boundary, HDB Property Information, Business, Entertn, F&B, FinServ, Leisure&Recreation and Retails. Aspatial data: HDB Property Information. This data is for us to use.

Mmethodology :

1,Prepare hexagonal data. 2,Draw the flow data map for Saturday morning. 3,Prepare the destination data for customer activities on Saturday. 4,Data integration. 5,Model. 6,Visualization. 7, Limitation

1,Prepare hexagonal data.

pacman::p_load(tmap, sf, DT, stplanr, sp, dplyr,
               performance, reshape2, units, 
               ggpubr, tidyverse, mapview, httr, sfheaders, knitr, kableExtra)

Importing the OD data

odbus <- read_csv("data/aspatial/origin_destination_bus_202310.csv")
Rows: 5694297 Columns: 7
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (5): YEAR_MONTH, DAY_TYPE, PT_TYPE, ORIGIN_PT_CODE, DESTINATION_PT_CODE
dbl (2): TIME_PER_HOUR, TOTAL_TRIPS

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
odbus$ORIGIN_PT_CODE <- as.factor(odbus$ORIGIN_PT_CODE)
odbus$DESTINATION_PT_CODE <- as.factor(odbus$DESTINATION_PT_CODE) 
glimpse(odbus)
Rows: 5,694,297
Columns: 7
$ YEAR_MONTH          <chr> "2023-10", "2023-10", "2023-10", "2023-10", "2023-…
$ DAY_TYPE            <chr> "WEEKENDS/HOLIDAY", "WEEKDAY", "WEEKENDS/HOLIDAY",…
$ TIME_PER_HOUR       <dbl> 16, 16, 14, 14, 17, 17, 17, 7, 14, 14, 10, 20, 20,…
$ PT_TYPE             <chr> "BUS", "BUS", "BUS", "BUS", "BUS", "BUS", "BUS", "…
$ ORIGIN_PT_CODE      <fct> 04168, 04168, 80119, 80119, 44069, 20281, 20281, 1…
$ DESTINATION_PT_CODE <fct> 10051, 10051, 90079, 90079, 17229, 20141, 20141, 1…
$ TOTAL_TRIPS         <dbl> 3, 5, 3, 5, 4, 1, 24, 2, 1, 7, 3, 2, 5, 1, 1, 1, 1…
weekendmorning11_14 <- odbus %>%
  filter(DAY_TYPE == "WEEKENDS/HOLIDAY") %>%
  filter(TIME_PER_HOUR >= 11 & TIME_PER_HOUR <= 14) %>%
  group_by(ORIGIN_PT_CODE, DESTINATION_PT_CODE) %>%
  summarise(TRIPS = sum(TOTAL_TRIPS), .groups = 'keep')
datatable(weekendmorning11_14)
Warning in instance$preRenderHook(instance): It seems your data is too big for
client-side DataTables. You may consider server-side processing:
https://rstudio.github.io/DT/server.html
write_rds(weekendmorning11_14, "data/rds/weekendmorning11_14.rds")
weekendmorning11_14 <- read_rds("data/rds/weekendmorning11_14.rds")

busstop points

busstop <- st_read(dsn = "data/geospatial", layer = "BusStop") %>%
  st_transform(crs = 3414)
Reading layer `BusStop' from data source 
  `/Users/linxu/ISSS624/take home exercise 2/data/geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 5161 features and 3 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 3970.122 ymin: 26482.1 xmax: 48284.56 ymax: 52983.82
Projected CRS: SVY21
glimpse(busstop)
Rows: 5,161
Columns: 4
$ BUS_STOP_N <chr> "22069", "32071", "44331", "96081", "11561", "66191", "2338…
$ BUS_ROOF_N <chr> "B06", "B23", "B01", "B05", "B05", "B03", "B02A", "B02", "B…
$ LOC_DESC   <chr> "OPP CEVA LOGISTICS", "AFT TRACK 13", "BLK 239", "GRACE IND…
$ geometry   <POINT [m]> POINT (13576.31 32883.65), POINT (13228.59 44206.38),…
busstop_points = busstop %>%
  st_as_sf(coords = c("geometry"), crs = 3414, remove = FALSE)
mapview_busstop_points = mapview(busstop_points, cex = 0.5, alpha = .5, popup = NULL)
mapview_busstop_points
area_honeycomb_grid = st_make_grid(busstop_points, c(750, 750), what = "polygons", square = FALSE)
honeycomb_grid_sf = st_sf(area_honeycomb_grid) %>%
  mutate(grid_id = 1:length(lengths(area_honeycomb_grid)))
honeycomb_grid_sf$n_colli = lengths(st_intersects(honeycomb_grid_sf, busstop_points))
honeycomb_count = filter(honeycomb_grid_sf, n_colli > 0)
write_rds(honeycomb_count, "data/rds/honeycomb_count.rds")
map_honeycomb = tm_shape(honeycomb_count) +
  tm_fill(
    col = "n_colli",
    palette = "Reds",
    style = "cont",
    title = "Number of collisions",
    id = "grid_id",
    showNA = FALSE,
    alpha = 0.6,
    popup.vars = c(
      "Number of collisions: " = "n_colli"
    ),
    popup.format = list(
      n_colli = list(format = "f", digits = 0)
    )
  ) +
  tm_borders(col = "grey40", lwd = 0.7)
map_honeycomb

busstop_honeycomb_count <- st_intersection(busstop, honeycomb_count) %>%
  select(BUS_STOP_N, grid_id) %>%
  st_drop_geometry()
Warning: attribute variables are assumed to be spatially constant throughout
all geometries
glimpse(busstop_honeycomb_count)
Rows: 5,161
Columns: 2
$ BUS_STOP_N <chr> "25059", "25751", "26379", "26369", "25741", "26399", "2571…
$ grid_id    <int> 23, 44, 46, 46, 66, 67, 67, 67, 67, 68, 86, 87, 88, 88, 88,…
write_rds(busstop_honeycomb_count, "data/rds/busstop_honeycomb_count.rds")  

2,Draw the flow data map for Saturday morning.

weekendmorning11_14 <- left_join(weekendmorning11_14 , busstop_honeycomb_count,
            by = c("ORIGIN_PT_CODE" = "BUS_STOP_N")) %>%
  rename(ORIGIN_BS = ORIGIN_PT_CODE,
         ORIGIN_SZ = grid_id,
         DESTIN_BS = DESTINATION_PT_CODE)
Warning in left_join(weekendmorning11_14, busstop_honeycomb_count, by = c(ORIGIN_PT_CODE = "BUS_STOP_N")): Detected an unexpected many-to-many relationship between `x` and `y`.
ℹ Row 27736 of `x` matches multiple rows in `y`.
ℹ Row 3057 of `y` matches multiple rows in `x`.
ℹ If a many-to-many relationship is expected, set `relationship =
  "many-to-many"` to silence this warning.
duplicate <- weekendmorning11_14 %>%
  group_by_all() %>%
  filter(n()>1) %>%
  ungroup()
weekendmorning11_14 <- unique(weekendmorning11_14)
weekendmorning11_14 <- left_join(weekendmorning11_14 , busstop_honeycomb_count,
            by = c("DESTIN_BS" = "BUS_STOP_N")) 
Warning in left_join(weekendmorning11_14, busstop_honeycomb_count, by = c(DESTIN_BS = "BUS_STOP_N")): Detected an unexpected many-to-many relationship between `x` and `y`.
ℹ Row 206 of `x` matches multiple rows in `y`.
ℹ Row 3146 of `y` matches multiple rows in `x`.
ℹ If a many-to-many relationship is expected, set `relationship =
  "many-to-many"` to silence this warning.
duplicate <- weekendmorning11_14 %>%
  group_by_all() %>%
  filter(n()>1) %>%
  ungroup()
weekendmorning11_14 <- unique(weekendmorning11_14)
weekendmorning11_14 <- weekendmorning11_14 %>%
  rename(DESTIN_SZ = grid_id) %>%
  drop_na() %>%
  group_by(ORIGIN_SZ, DESTIN_SZ) %>%
  summarise(WEEKENDDAYMORNING_PEAK = sum(TRIPS))
`summarise()` has grouped output by 'ORIGIN_SZ'. You can override using the
`.groups` argument.
write_rds(weekendmorning11_14, "data/rds/weekendmorning11_14.rds")
weekendmorning11_14 <- read_rds("data/rds/weekendmorning11_14.rds")
weekendmorning11_14_1 <- weekendmorning11_14[weekendmorning11_14$ORIGIN_SZ!=weekendmorning11_14$DESTIN_SZ,]
flowLine <- od2line(flow = weekendmorning11_14_1, 
                    zones = honeycomb_count,
                    zone_code = "grid_id")
Creating centroids representing desire line start and end points.
tm_shape(honeycomb_count) +
  tm_polygons() +
flowLine %>%  
tm_shape() +
  tm_lines(lwd = "WEEKENDDAYMORNING_PEAK",
           style = "quantile",
           scale = c(0.1, 1, 3, 5, 7, 10),
           n = 6,
           alpha = 0.3)
Warning in g$scale * (w_legend/maxW): longer object length is not a multiple of
shorter object length
Warning in g$scale * (x/maxW): longer object length is not a multiple of
shorter object length

tm_shape(honeycomb_count) +
  tm_polygons() +
flowLine %>%  
  filter(WEEKENDDAYMORNING_PEAK >= 2000) %>%
tm_shape() +
  tm_lines(lwd = "WEEKENDDAYMORNING_PEAK",
           style = "quantile",
           scale = c(0.1, 1, 3, 5, 7, 10),
           n = 6,
           alpha = 0.3)
Warning in g$scale * (w_legend/maxW): longer object length is not a multiple of
shorter object length

Caculate the distance

honeycomb_count <- read_rds("data/rds/honeycomb_count.rds")
honeycomb_count
Simple feature collection with 834 features and 2 fields
Geometry type: POLYGON
Dimension:     XY
Bounding box:  xmin: 3595.122 ymin: 26049.09 xmax: 48595.12 ymax: 53545.39
Projected CRS: SVY21 / Singapore TM
First 10 features:
              area_honeycomb_grid grid_id n_colli
1  POLYGON ((3970.122 27348.13...      23       1
2  POLYGON ((4345.122 27997.65...      44       1
3  POLYGON ((4345.122 30595.72...      46       2
4  POLYGON ((4720.122 28647.16...      66       1
5  POLYGON ((4720.122 29946.2,...      67       4
6  POLYGON ((4720.122 31245.24...      68       1
7  POLYGON ((5095.122 27997.65...      86       1
8  POLYGON ((5095.122 29296.68...      87       1
9  POLYGON ((5095.122 30595.72...      88       4
10 POLYGON ((5095.122 31894.76...      89       2
honeycomb_count_sp <- as(honeycomb_count, "Spatial")
honeycomb_count_sp
class       : SpatialPolygonsDataFrame 
features    : 834 
extent      : 3595.122, 48595.12, 26049.09, 53545.39  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 
variables   : 2
names       : grid_id, n_colli 
min values  :      23,       1 
max values  :    2505,      19 
dist <- spDists(honeycomb_count_sp, 
                longlat = FALSE)
head(dist, n=c(10, 10))
          [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
 [1,]    0.000  750.000 3269.174 1500.000 2704.163 3968.627 1299.038 2250.000
 [2,]  750.000    0.000 2598.076  750.000 1984.313 3269.174  750.000 1500.000
 [3,] 3269.174 2598.076    0.000 1984.313  750.000  750.000 2704.163 1500.000
 [4,] 1500.000  750.000 1984.313    0.000 1299.038 2598.076  750.000  750.000
 [5,] 2704.163 1984.313  750.000 1299.038    0.000 1299.038 1984.313  750.000
 [6,] 3968.627 3269.174  750.000 2598.076 1299.038    0.000 3269.174 1984.313
 [7,] 1299.038  750.000 2704.163  750.000 1984.313 3269.174    0.000 1299.038
 [8,] 2250.000 1500.000 1500.000  750.000  750.000 1984.313 1299.038    0.000
 [9,] 3436.932 2704.163  750.000 1984.313  750.000  750.000 2598.076 1299.038
[10,] 4683.748 3968.627 1500.000 3269.174 1984.313  750.000 3897.114 2598.076
          [,9]    [,10]
 [1,] 3436.932 4683.748
 [2,] 2704.163 3968.627
 [3,]  750.000 1500.000
 [4,] 1984.313 3269.174
 [5,]  750.000 1984.313
 [6,]  750.000  750.000
 [7,] 2598.076 3897.114
 [8,] 1299.038 2598.076
 [9,]    0.000 1299.038
[10,] 1299.038    0.000
sz_names <- honeycomb_count$grid_id
colnames(dist) <- paste0(sz_names)
rownames(dist) <- paste0(sz_names)
distPair <- melt(dist) %>%
  rename(dist = value)
head(distPair, 10)
   Var1 Var2     dist
1    23   23    0.000
2    44   23  750.000
3    46   23 3269.174
4    66   23 1500.000
5    67   23 2704.163
6    68   23 3968.627
7    86   23 1299.038
8    87   23 2250.000
9    88   23 3436.932
10   89   23 4683.748
distPair %>%
  filter(dist > 0) %>%
  summary()
      Var1           Var2           dist      
 Min.   :  23   Min.   :  23   Min.   :  750  
 1st Qu.: 871   1st Qu.: 871   1st Qu.: 8352  
 Median :1324   Median :1324   Median :13332  
 Mean   :1269   Mean   :1269   Mean   :14162  
 3rd Qu.:1688   3rd Qu.:1688   3rd Qu.:18929  
 Max.   :2505   Max.   :2505   Max.   :44680  
distPair$dist <- ifelse(distPair$dist == 0,
                        50, distPair$dist)
distPair %>%
  summary()
      Var1           Var2           dist      
 Min.   :  23   Min.   :  23   Min.   :   50  
 1st Qu.: 871   1st Qu.: 871   1st Qu.: 8250  
 Median :1324   Median :1324   Median :13332  
 Mean   :1269   Mean   :1269   Mean   :14145  
 3rd Qu.:1688   3rd Qu.:1688   3rd Qu.:18929  
 Max.   :2505   Max.   :2505   Max.   :44680  
distPair <- distPair %>%
  rename(orig = Var1,
         dest = Var2)
write_rds(distPair, "data/rds/distPair.rds") 
weekendmorning11_14 <- read_rds("data/rds/weekendmorning11_14.rds")
flow_data <- weekendmorning11_14 %>%
  group_by(ORIGIN_SZ, DESTIN_SZ) %>% 
  summarize(TRIPS = sum(WEEKENDDAYMORNING_PEAK)) 
`summarise()` has grouped output by 'ORIGIN_SZ'. You can override using the
`.groups` argument.
head(flow_data)
# A tibble: 6 × 3
# Groups:   ORIGIN_SZ [2]
  ORIGIN_SZ DESTIN_SZ TRIPS
      <int>     <int> <dbl>
1        44       128     4
2        44       129     2
3        44       175    20
4        46        67     2
5        46       111     6
6        46       134    73
flow_data$FlowNoIntra <- ifelse(
  flow_data$ORIGIN_SZ == flow_data$DESTIN_SZ, 
  0, flow_data$TRIPS)
flow_data$offset <- ifelse(
  flow_data$ORIGIN_SZ == flow_data$DESTIN_SZ, 
  0.000001, 1)
flow_data$ORIGIN_SZ <- as.integer(flow_data$ORIGIN_SZ)
flow_data$DESTIN_SZ <- as.integer(flow_data$DESTIN_SZ)
distPair$orig <- as.integer(distPair$orig)
distPair$dest <- as.integer(distPair$dest)
distPair$dist <- as.integer(distPair$dist)
flow_data1 <- flow_data %>%
  left_join (distPair,
             by = c("ORIGIN_SZ" = "orig",
                    "DESTIN_SZ" = "dest"))
glimpse(flow_data1)
Rows: 62,398
Columns: 6
Groups: ORIGIN_SZ [821]
$ ORIGIN_SZ   <int> 44, 44, 44, 46, 46, 46, 46, 46, 66, 66, 66, 67, 67, 67, 67…
$ DESTIN_SZ   <int> 128, 129, 175, 67, 111, 134, 155, 406, 44, 134, 175, 44, 8…
$ TRIPS       <dbl> 4, 2, 20, 2, 6, 73, 12, 35, 2, 1, 18, 3, 7, 1, 25, 28, 1, …
$ FlowNoIntra <dbl> 4, 2, 20, 2, 6, 73, 12, 35, 2, 1, 18, 3, 7, 1, 25, 28, 1, …
$ offset      <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…
$ dist        <int> 1499, 1984, 6873, 749, 2250, 5408, 4918, 7154, 750, 7232, …
flow_data1 <- flow_data1 %>%
  left_join(honeycomb_count,
            by = c("DESTIN_SZ" = "grid_id")) %>%
  rename(DIST = dist)
summary(flow_data1)
   ORIGIN_SZ      DESTIN_SZ        TRIPS          FlowNoIntra     
 Min.   :  44   Min.   :  44   Min.   :    1.0   Min.   :    0.0  
 1st Qu.:1119   1st Qu.:1119   1st Qu.:    4.0   1st Qu.:    4.0  
 Median :1435   Median :1435   Median :   14.0   Median :   14.0  
 Mean   :1423   Mean   :1423   Mean   :  120.5   Mean   :  115.7  
 3rd Qu.:1727   3rd Qu.:1727   3rd Qu.:   58.0   3rd Qu.:   56.0  
 Max.   :2505   Max.   :2505   Max.   :43418.0   Max.   :43418.0  
     offset              DIST          area_honeycomb_grid    n_colli      
 Min.   :0.000001   Min.   :   50   POLYGON      :62398    Min.   : 1.000  
 1st Qu.:1.000000   1st Qu.: 2704   epsg:3414    :    0    1st Qu.: 5.000  
 Median :1.000000   Median : 5250   +proj=tmer...:    0    Median : 8.000  
 Mean   :0.990865   Mean   : 6224                          Mean   : 7.929  
 3rd Qu.:1.000000   3rd Qu.: 8649                          3rd Qu.:10.000  
 Max.   :1.000000   Max.   :24784                          Max.   :19.000  
write_rds(flow_data1,
          "data/rds/flow_data1.rds")

#3,Prepare the destination data for customer activities on Saturday.

Schools

url<-"https://www.onemap.gov.sg/api/common/elastic/search"

csv<-read_csv("data/aspatial/Generalinformationofschools.csv")
Rows: 346 Columns: 31
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (31): school_name, url_address, address, postal_code, telephone_no, tele...

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
postcodes<-csv$`postal_code`

found<-data.frame()
not_found<-data.frame()

for(postcode in postcodes){
  query<-list('searchVal'=postcode,'returnGeom'='Y','getAddrDetails'='Y','pageNum'='1')
  res<- GET(url,query=query)
  
  if((content(res)$found)!=0){
    found<-rbind(found,data.frame(content(res))[4:13])
  } else{
    not_found = data.frame(postcode)
  }
}
merged = merge(csv, found, by.x = 'postal_code', by.y = 'results.POSTAL', all = TRUE)
write.csv(merged, file = "data/aspatial/schools.csv")
write.csv(not_found, file = "data/aspatial/not_found.csv")
schools <- read_csv("data/aspatial/schools.csv") %>%
  rename(latitude = "results.LATITUDE",
         longitude = "results.LONGITUDE")%>%
  select(postal_code, school_name, latitude, longitude)
New names:
Rows: 350 Columns: 41
── Column specification
──────────────────────────────────────────────────────── Delimiter: "," chr
(36): postal_code, school_name, url_address, address, telephone_no, tele... dbl
(5): ...1, results.X, results.Y, results.LATITUDE, results.LONGITUDE
ℹ Use `spec()` to retrieve the full column specification for this data. ℹ
Specify the column types or set `show_col_types = FALSE` to quiet this message.
• `` -> `...1`
schools <- schools[complete.cases(schools$longitude, schools$latitude), ]
schools_sf <- st_as_sf(schools, 
                       coords = c("longitude", "latitude"),
                       crs=4326) %>%
  st_transform(crs = 3414)
tmap_options(check.and.fix = TRUE)
tm_shape(honeycomb_count) +
  tm_polygons() +
tm_shape(schools_sf) +
  tm_dots()

tmap_mode("plot")
tmap mode set to plotting
honeycomb_count$`SCHOOL_COUNT`<- lengths(
  st_intersects(
   honeycomb_count, schools_sf))
summary(honeycomb_count$SCHOOL_COUNT)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.0000  0.0000  0.0000  0.4113  1.0000  4.0000 

RapidTransitSystemStation

RTSS_sf <- st_read(dsn = "data/geospatial/",
                layer = "RapidTransitSystemStation")%>%
  st_transform(crs = 3414)
Reading layer `RapidTransitSystemStation' from data source 
  `/Users/linxu/ISSS624/take home exercise 2/data/geospatial' 
  using driver `ESRI Shapefile'
Warning in CPL_read_ogr(dsn, layer, query, as.character(options), quiet, : GDAL
Message 1: Non closed ring detected. To avoid accepting it, set the
OGR_GEOMETRY_ACCEPT_UNCLOSED_RING configuration option to NO
Simple feature collection with 220 features and 4 fields
Geometry type: POLYGON
Dimension:     XY
Bounding box:  xmin: 6068.209 ymin: 27478.44 xmax: 45377.5 ymax: 47913.58
Projected CRS: SVY21
RTSS_sf_polygons <- RTSS_sf[st_is_valid(RTSS_sf), ]
RTSS_sf_points <- st_centroid(RTSS_sf_polygons)
Warning: st_centroid assumes attributes are constant over geometries
tmap_options(check.and.fix = TRUE)
tm_shape(honeycomb_count) +
  tm_polygons() +
tm_shape(RTSS_sf_points) +
  tm_dots()
Warning: The shape RTSS_sf_points contains empty units.

tmap_mode("plot")
tmap mode set to plotting
honeycomb_count$`RTSS_COUNT`<- lengths(
  st_intersects(
    honeycomb_count, RTSS_sf_points))
summary(honeycomb_count$`RTSS_COUNT`)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.0000  0.0000  0.0000  0.2542  0.0000  4.0000 

Entertn

entertn_sf <- st_read(dsn = "data/geospatial/",
                layer = "entertn")%>%
  st_transform(crs = 3414)
Reading layer `entertn' from data source 
  `/Users/linxu/ISSS624/take home exercise 2/data/geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 114 features and 3 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 10809.34 ymin: 26528.63 xmax: 41600.62 ymax: 46375.77
Projected CRS: SVY21 / Singapore TM
tmap_options(check.and.fix = TRUE)
tm_shape(honeycomb_count) +
  tm_polygons() +
tm_shape(entertn_sf) +
  tm_dots()

tmap_mode("plot")
tmap mode set to plotting
honeycomb_count$`ENTERTN_COUNT`<- lengths(
  st_intersects(
    honeycomb_count, entertn_sf))
summary(honeycomb_count$ENTERTN_COUNT)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.0000  0.0000  0.0000  0.1331  0.0000  9.0000 

Liesure&Recreation

lr_sf <- st_read(dsn = "data/geospatial/",
                                    layer = "Liesure&Recreation") %>%
  st_transform(crs = 3414)
Reading layer `Liesure&Recreation' from data source 
  `/Users/linxu/ISSS624/take home exercise 2/data/geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 1217 features and 30 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 6010.495 ymin: 25134.28 xmax: 48439.77 ymax: 50078.88
Projected CRS: SVY21 / Singapore TM
tmap_options(check.and.fix = TRUE)
tm_shape(honeycomb_count) +
  tm_polygons() +
tm_shape(lr_sf) +
  tm_dots()

tmap_mode("plot")
tmap mode set to plotting
honeycomb_count$`LR_COUNT`<- lengths(
  st_intersects(
    honeycomb_count, lr_sf))
summary(honeycomb_count$LR_COUNT)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  0.000   0.000   0.000   1.307   1.000  41.000 

Retails

retails_sf <- st_read(dsn = "data/geospatial/",
                layer = "Retails")%>%
  st_transform(crs = 3414)
Reading layer `Retails' from data source 
  `/Users/linxu/ISSS624/take home exercise 2/data/geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 37635 features and 3 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 4737.982 ymin: 25171.88 xmax: 48265.04 ymax: 50135.28
Projected CRS: SVY21 / Singapore TM
tmap_options(check.and.fix = TRUE)
tm_shape(honeycomb_count) +
  tm_polygons() +
tm_shape(retails_sf) +
  tm_dots()

tmap_mode("plot")
tmap mode set to plotting
honeycomb_count$`RETAILS_COUNT`<- lengths(
  st_intersects(
    honeycomb_count, retails_sf))
glimpse(honeycomb_count$RETAILS_COUNT)
 int [1:834] 0 0 0 0 5 0 0 0 5 1 ...

4,Data integration.

honeycomb_count_tidy <- honeycomb_count %>%
  st_drop_geometry() %>%
  select(grid_id, SCHOOL_COUNT, RTSS_COUNT, ENTERTN_COUNT, LR_COUNT, RETAILS_COUNT)
flow_data2 <- flow_data1 %>%
  left_join(honeycomb_count_tidy,
            by = c("DESTIN_SZ" = "grid_id")) 
glimpse(flow_data2)
Rows: 62,398
Columns: 13
Groups: ORIGIN_SZ [821]
$ ORIGIN_SZ           <int> 44, 44, 44, 46, 46, 46, 46, 46, 66, 66, 66, 67, 67…
$ DESTIN_SZ           <int> 128, 129, 175, 67, 111, 134, 155, 406, 44, 134, 17…
$ TRIPS               <dbl> 4, 2, 20, 2, 6, 73, 12, 35, 2, 1, 18, 3, 7, 1, 25,…
$ FlowNoIntra         <dbl> 4, 2, 20, 2, 6, 73, 12, 35, 2, 1, 18, 3, 7, 1, 25,…
$ offset              <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,…
$ DIST                <int> 1499, 1984, 6873, 749, 2250, 5408, 4918, 7154, 750…
$ area_honeycomb_grid <POLYGON [m]> POLYGON ((5845.122 27997.65..., POLYGON ((…
$ n_colli             <int> 1, 1, 11, 4, 5, 1, 5, 9, 1, 1, 11, 1, 4, 2, 5, 1, …
$ SCHOOL_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$ RTSS_COUNT          <int> 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0,…
$ ENTERTN_COUNT       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$ LR_COUNT            <int> 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,…
$ RETAILS_COUNT       <int> 0, 0, 2, 5, 4, 3, 0, 16, 0, 3, 2, 0, 5, 1, 4, 0, 3…
flow_data2$SCHOOL_COUNT <- ifelse(
  flow_data2$SCHOOL_COUNT == 0,
  0.99, flow_data2$SCHOOL_COUNT)
flow_data2$RTSS_COUNT <- ifelse(
  flow_data2$RTSS_COUNT == 0,
  0.99, flow_data2$RTSS_COUNT)
flow_data2$ENTERTN_COUNT <- ifelse(
  flow_data2$ENTERTN_COUNT == 0,
  0.99, flow_data2$ENTERTN_COUNT)
flow_data2$LR_COUNT <- ifelse(
  flow_data2$LR_COUNT == 0,
  0.99, flow_data2$LR_COUNT)
flow_data2$RETAILS_COUNT <- ifelse(
  flow_data2$RETAILS_COUNT == 0,
  0.99, flow_data2$RETAILS_COUNT)
summary(flow_data2)
   ORIGIN_SZ      DESTIN_SZ        TRIPS          FlowNoIntra     
 Min.   :  44   Min.   :  44   Min.   :    1.0   Min.   :    0.0  
 1st Qu.:1119   1st Qu.:1119   1st Qu.:    4.0   1st Qu.:    4.0  
 Median :1435   Median :1435   Median :   14.0   Median :   14.0  
 Mean   :1423   Mean   :1423   Mean   :  120.5   Mean   :  115.7  
 3rd Qu.:1727   3rd Qu.:1727   3rd Qu.:   58.0   3rd Qu.:   56.0  
 Max.   :2505   Max.   :2505   Max.   :43418.0   Max.   :43418.0  
     offset              DIST          area_honeycomb_grid    n_colli      
 Min.   :0.000001   Min.   :   50   POLYGON      :62398    Min.   : 1.000  
 1st Qu.:1.000000   1st Qu.: 2704   epsg:3414    :    0    1st Qu.: 5.000  
 Median :1.000000   Median : 5250   +proj=tmer...:    0    Median : 8.000  
 Mean   :0.990865   Mean   : 6224                          Mean   : 7.929  
 3rd Qu.:1.000000   3rd Qu.: 8649                          3rd Qu.:10.000  
 Max.   :1.000000   Max.   :24784                          Max.   :19.000  
  SCHOOL_COUNT     RTSS_COUNT    ENTERTN_COUNT      LR_COUNT     
 Min.   :0.990   Min.   :0.990   Min.   :0.990   Min.   : 0.990  
 1st Qu.:0.990   1st Qu.:0.990   1st Qu.:0.990   1st Qu.: 0.990  
 Median :0.990   Median :0.990   Median :0.990   Median : 1.000  
 Mean   :1.178   Mean   :1.125   Mean   :1.183   Mean   : 2.703  
 3rd Qu.:1.000   3rd Qu.:1.000   3rd Qu.:0.990   3rd Qu.: 3.000  
 Max.   :4.000   Max.   :4.000   Max.   :9.000   Max.   :41.000  
 RETAILS_COUNT    
 Min.   :   0.99  
 1st Qu.:   7.00  
 Median :  30.00  
 Mean   :  96.65  
 3rd Qu.: 107.00  
 Max.   :1678.00  
write_rds(flow_data2,
          "data/rds/flow_data_tidy.rds")
flow_data3 <- read_rds("data/rds/flow_data_tidy.rds")
flow_data3 <- flow_data2 %>%
  mutate(ORIGIN_SZ = as.character(ORIGIN_SZ), DESTIN_SZ = as.character(DESTIN_SZ))
glimpse(flow_data3)
Rows: 62,398
Columns: 13
Groups: ORIGIN_SZ [821]
$ ORIGIN_SZ           <chr> "44", "44", "44", "46", "46", "46", "46", "46", "6…
$ DESTIN_SZ           <chr> "128", "129", "175", "67", "111", "134", "155", "4…
$ TRIPS               <dbl> 4, 2, 20, 2, 6, 73, 12, 35, 2, 1, 18, 3, 7, 1, 25,…
$ FlowNoIntra         <dbl> 4, 2, 20, 2, 6, 73, 12, 35, 2, 1, 18, 3, 7, 1, 25,…
$ offset              <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,…
$ DIST                <int> 1499, 1984, 6873, 749, 2250, 5408, 4918, 7154, 750…
$ area_honeycomb_grid <POLYGON [m]> POLYGON ((5845.122 27997.65..., POLYGON ((…
$ n_colli             <int> 1, 1, 11, 4, 5, 1, 5, 9, 1, 1, 11, 1, 4, 2, 5, 1, …
$ SCHOOL_COUNT        <dbl> 0.99, 0.99, 0.99, 0.99, 0.99, 0.99, 0.99, 0.99, 0.…
$ RTSS_COUNT          <dbl> 0.99, 0.99, 1.00, 0.99, 0.99, 0.99, 1.00, 1.00, 0.…
$ ENTERTN_COUNT       <dbl> 0.99, 0.99, 0.99, 0.99, 0.99, 0.99, 0.99, 0.99, 0.…
$ LR_COUNT            <dbl> 0.99, 0.99, 0.99, 0.99, 0.99, 1.00, 0.99, 0.99, 0.…
$ RETAILS_COUNT       <dbl> 0.99, 0.99, 2.00, 5.00, 4.00, 3.00, 0.99, 16.00, 0…
kable(head(flow_data3[, 1:5], n = 5))
ORIGIN_SZ DESTIN_SZ TRIPS FlowNoIntra offset
44 128 4 4 1
44 129 2 2 1
44 175 20 20 1
46 67 2 2 1
46 111 6 6 1
flow_data3$FlowNoIntra <- ifelse(
  flow_data3$ORIGIN_SZ == flow_data3$DESTIN_SZ, 
  0, flow_data3$TRIPS)
flow_data3$offset <- ifelse(
  flow_data3$ORIGIN_SZ == flow_data3$DESTIN_SZ, 
  0.000001, 1)
inter_zonal_flow <- flow_data3 %>%
  filter(FlowNoIntra > 0)
glimpse(inter_zonal_flow)
Rows: 61,828
Columns: 13
Groups: ORIGIN_SZ [821]
$ ORIGIN_SZ           <chr> "44", "44", "44", "46", "46", "46", "46", "46", "6…
$ DESTIN_SZ           <chr> "128", "129", "175", "67", "111", "134", "155", "4…
$ TRIPS               <dbl> 4, 2, 20, 2, 6, 73, 12, 35, 2, 1, 18, 3, 7, 1, 25,…
$ FlowNoIntra         <dbl> 4, 2, 20, 2, 6, 73, 12, 35, 2, 1, 18, 3, 7, 1, 25,…
$ offset              <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,…
$ DIST                <int> 1499, 1984, 6873, 749, 2250, 5408, 4918, 7154, 750…
$ area_honeycomb_grid <POLYGON [m]> POLYGON ((5845.122 27997.65..., POLYGON ((…
$ n_colli             <int> 1, 1, 11, 4, 5, 1, 5, 9, 1, 1, 11, 1, 4, 2, 5, 1, …
$ SCHOOL_COUNT        <dbl> 0.99, 0.99, 0.99, 0.99, 0.99, 0.99, 0.99, 0.99, 0.…
$ RTSS_COUNT          <dbl> 0.99, 0.99, 1.00, 0.99, 0.99, 0.99, 1.00, 1.00, 0.…
$ ENTERTN_COUNT       <dbl> 0.99, 0.99, 0.99, 0.99, 0.99, 0.99, 0.99, 0.99, 0.…
$ LR_COUNT            <dbl> 0.99, 0.99, 0.99, 0.99, 0.99, 1.00, 0.99, 0.99, 0.…
$ RETAILS_COUNT       <dbl> 0.99, 0.99, 2.00, 5.00, 4.00, 3.00, 0.99, 16.00, 0…

5,Model

Origin_Constrained model

orcSIM_Poisson <- glm(formula = TRIPS ~ 
                ORIGIN_SZ +
                log(SCHOOL_COUNT) +  
                log(ENTERTN_COUNT) +
                log(RTSS_COUNT) + 
                log(LR_COUNT) +
                log(RETAILS_COUNT) +
                log(DIST) - 1,
              family = poisson(link = "log"),
              data = inter_zonal_flow,
              na.action = na.exclude)
summary(orcSIM_Poisson)

Call:
glm(formula = TRIPS ~ ORIGIN_SZ + log(SCHOOL_COUNT) + log(ENTERTN_COUNT) + 
    log(RTSS_COUNT) + log(LR_COUNT) + log(RETAILS_COUNT) + log(DIST) - 
    1, family = poisson(link = "log"), data = inter_zonal_flow, 
    na.action = na.exclude)

Coefficients:
                     Estimate Std. Error  z value Pr(>|z|)    
ORIGIN_SZ1001      13.9522257  0.0481911   289.52   <2e-16 ***
ORIGIN_SZ1003      16.5614723  0.0074577  2220.74   <2e-16 ***
ORIGIN_SZ1004      16.8635747  0.0072645  2321.38   <2e-16 ***
ORIGIN_SZ1011      13.8901017  0.0368240   377.20   <2e-16 ***
ORIGIN_SZ1012      14.7621749  0.0239745   615.75   <2e-16 ***
ORIGIN_SZ1013      14.4064067  0.0199029   723.83   <2e-16 ***
ORIGIN_SZ1014      14.3918837  0.0184347   780.70   <2e-16 ***
ORIGIN_SZ1015      13.7171479  0.0263921   519.75   <2e-16 ***
ORIGIN_SZ1016      15.7463647  0.0093067  1691.94   <2e-16 ***
ORIGIN_SZ1018      15.2690538  0.0201405   758.13   <2e-16 ***
ORIGIN_SZ1019      16.9424129  0.0082493  2053.79   <2e-16 ***
ORIGIN_SZ1023      15.1842163  0.0191954   791.03   <2e-16 ***
ORIGIN_SZ1024      16.3446959  0.0091104  1794.08   <2e-16 ***
ORIGIN_SZ1025      13.4718382  0.0536448   251.13   <2e-16 ***
ORIGIN_SZ1033      14.6499350  0.0173378   844.97   <2e-16 ***
ORIGIN_SZ1034      15.2168146  0.0122121  1246.04   <2e-16 ***
ORIGIN_SZ1035      15.3979009  0.0109772  1402.72   <2e-16 ***
ORIGIN_SZ1036      15.4696030  0.0110899  1394.92   <2e-16 ***
ORIGIN_SZ1037      15.3548825  0.0103197  1487.93   <2e-16 ***
ORIGIN_SZ1043      15.5737689  0.0206645   753.65   <2e-16 ***
ORIGIN_SZ1045      16.3356712  0.0080020  2041.44   <2e-16 ***
ORIGIN_SZ1046      16.2164649  0.0096998  1671.84   <2e-16 ***
ORIGIN_SZ1053      14.9450437  0.0135442  1103.43   <2e-16 ***
ORIGIN_SZ1054      14.3737794  0.0180907   794.54   <2e-16 ***
ORIGIN_SZ1055      15.6201549  0.0098605  1584.11   <2e-16 ***
ORIGIN_SZ1056      14.7422819  0.0155813   946.15   <2e-16 ***
ORIGIN_SZ1064      13.1960411  0.1796497    73.45   <2e-16 ***
ORIGIN_SZ1066      16.4904787  0.0075434  2186.09   <2e-16 ***
ORIGIN_SZ1067      15.0011162  0.0215949   694.66   <2e-16 ***
ORIGIN_SZ1074      14.9653575  0.0141761  1055.67   <2e-16 ***
ORIGIN_SZ1075      13.1867670  0.0353658   372.87   <2e-16 ***
ORIGIN_SZ1076      14.5056392  0.0152828   949.15   <2e-16 ***
ORIGIN_SZ1077      14.4224563  0.0189463   761.23   <2e-16 ***
ORIGIN_SZ1079      15.3679551  0.0110576  1389.81   <2e-16 ***
ORIGIN_SZ1085      13.0115857  0.1043134   124.74   <2e-16 ***
ORIGIN_SZ1087      15.6005199  0.0121817  1280.65   <2e-16 ***
ORIGIN_SZ1088      14.3097821  0.0233528   612.77   <2e-16 ***
ORIGIN_SZ109       14.7306481  0.1032158   142.72   <2e-16 ***
ORIGIN_SZ1094      12.9356281  0.0825621   156.68   <2e-16 ***
ORIGIN_SZ1095      13.2564397  0.0535590   247.51   <2e-16 ***
ORIGIN_SZ1096      13.4953340  0.0510736   264.23   <2e-16 ***
ORIGIN_SZ1097      16.0412821  0.0074435  2155.06   <2e-16 ***
ORIGIN_SZ1098      13.6072833  0.0317402   428.71   <2e-16 ***
ORIGIN_SZ1099      15.1281740  0.0120480  1255.66   <2e-16 ***
ORIGIN_SZ110       15.1219984  0.0774656   195.21   <2e-16 ***
ORIGIN_SZ1105      16.1984686  0.0194475   832.93   <2e-16 ***
ORIGIN_SZ1106      12.2541101  0.1474864    83.09   <2e-16 ***
ORIGIN_SZ1107      14.2678299  0.0382472   373.04   <2e-16 ***
ORIGIN_SZ1108      17.7342041  0.0048102  3686.75   <2e-16 ***
ORIGIN_SZ1109      15.1083437  0.0216983   696.29   <2e-16 ***
ORIGIN_SZ111       17.0334941  0.0144287  1180.53   <2e-16 ***
ORIGIN_SZ1116      14.1947917  0.0199302   712.23   <2e-16 ***
ORIGIN_SZ1117      13.9156612  0.0238805   582.72   <2e-16 ***
ORIGIN_SZ1118      13.2485570  0.0359039   369.00   <2e-16 ***
ORIGIN_SZ1119      14.7977994  0.0137204  1078.53   <2e-16 ***
ORIGIN_SZ112       13.0830540  0.1644403    79.56   <2e-16 ***
ORIGIN_SZ1120      14.1557789  0.0235980   599.87   <2e-16 ***
ORIGIN_SZ1129      16.2752021  0.0095842  1698.12   <2e-16 ***
ORIGIN_SZ1130      16.2138007  0.0085591  1894.34   <2e-16 ***
ORIGIN_SZ1131      15.9415715  0.0153221  1040.43   <2e-16 ***
ORIGIN_SZ1136      13.9627811  0.0229093   609.48   <2e-16 ***
ORIGIN_SZ1138      13.2037742  0.0416333   317.14   <2e-16 ***
ORIGIN_SZ1139      15.4167264  0.0092889  1659.70   <2e-16 ***
ORIGIN_SZ1141      15.0360850  0.0126151  1191.91   <2e-16 ***
ORIGIN_SZ1148      13.5748855  0.0672193   201.95   <2e-16 ***
ORIGIN_SZ1149      15.0791558  0.0229876   655.97   <2e-16 ***
ORIGIN_SZ1150      16.2855386  0.0079447  2049.88   <2e-16 ***
ORIGIN_SZ1151      15.3582117  0.0135643  1132.26   <2e-16 ***
ORIGIN_SZ1158      13.8998961  0.0207454   670.02   <2e-16 ***
ORIGIN_SZ1159      14.9926805  0.0110821  1352.88   <2e-16 ***
ORIGIN_SZ1160      15.8790377  0.0075287  2109.15   <2e-16 ***
ORIGIN_SZ1171      16.6072668  0.0083655  1985.21   <2e-16 ***
ORIGIN_SZ1172      16.6874063  0.0072017  2317.16   <2e-16 ***
ORIGIN_SZ1173      14.7019854  0.0219763   668.99   <2e-16 ***
ORIGIN_SZ1174      11.7840329  0.2500211    47.13   <2e-16 ***
ORIGIN_SZ1178      14.6744515  0.0137059  1070.67   <2e-16 ***
ORIGIN_SZ1179      15.1569004  0.0102417  1479.92   <2e-16 ***
ORIGIN_SZ1180      15.8217666  0.0076215  2075.95   <2e-16 ***
ORIGIN_SZ1181      14.8320499  0.0121483  1220.91   <2e-16 ***
ORIGIN_SZ1183      14.2485588  0.0198987   716.05   <2e-16 ***
ORIGIN_SZ1190      13.2554271  0.0713408   185.80   <2e-16 ***
ORIGIN_SZ1192      16.1399854  0.0104477  1544.83   <2e-16 ***
ORIGIN_SZ1193      15.5155521  0.0113983  1361.21   <2e-16 ***
ORIGIN_SZ1194      14.7597132  0.0231139   638.56   <2e-16 ***
ORIGIN_SZ1200      14.5887416  0.0141517  1030.88   <2e-16 ***
ORIGIN_SZ1201      15.1733548  0.0102789  1476.17   <2e-16 ***
ORIGIN_SZ1203      15.3135542  0.0105726  1448.42   <2e-16 ***
ORIGIN_SZ1204      14.2864261  0.0178663   799.63   <2e-16 ***
ORIGIN_SZ1211      14.6746695  0.0463676   316.49   <2e-16 ***
ORIGIN_SZ1214      16.1406442  0.0091659  1760.94   <2e-16 ***
ORIGIN_SZ1215      14.0992543  0.0569978   247.37   <2e-16 ***
ORIGIN_SZ1216      14.2341886  0.0392631   362.53   <2e-16 ***
ORIGIN_SZ1220      15.4617819  0.0092665  1668.57   <2e-16 ***
ORIGIN_SZ1221      15.3176049  0.0088374  1733.26   <2e-16 ***
ORIGIN_SZ1222      15.1878051  0.0181221   838.08   <2e-16 ***
ORIGIN_SZ1223      14.2114286  0.0187550   757.74   <2e-16 ***
ORIGIN_SZ1224      14.4397810  0.0158946   908.47   <2e-16 ***
ORIGIN_SZ1231      13.5328698  0.0663222   204.05   <2e-16 ***
ORIGIN_SZ1232      14.4167133  0.0582521   247.49   <2e-16 ***
ORIGIN_SZ1235      14.0423707  0.0249757   562.24   <2e-16 ***
ORIGIN_SZ1236      14.6300171  0.0203411   719.23   <2e-16 ***
ORIGIN_SZ1241      14.5044303  0.0155848   930.68   <2e-16 ***
ORIGIN_SZ1242      14.6422056  0.0129363  1131.87   <2e-16 ***
ORIGIN_SZ1243      15.3653016  0.0087688  1752.26   <2e-16 ***
ORIGIN_SZ1246      14.9891797  0.0117892  1271.44   <2e-16 ***
ORIGIN_SZ1256      14.8985842  0.0165496   900.24   <2e-16 ***
ORIGIN_SZ1257      15.9234906  0.0112516  1415.22   <2e-16 ***
ORIGIN_SZ1258      14.9628527  0.0199634   749.51   <2e-16 ***
ORIGIN_SZ1262      14.1827295  0.0175103   809.96   <2e-16 ***
ORIGIN_SZ1263      15.6231572  0.0075547  2068.01   <2e-16 ***
ORIGIN_SZ1264      14.5502516  0.0161429   901.34   <2e-16 ***
ORIGIN_SZ1265      14.4706438  0.0161700   894.90   <2e-16 ***
ORIGIN_SZ1266      14.8963782  0.0141381  1053.63   <2e-16 ***
ORIGIN_SZ1267      14.4550799  0.0237579   608.43   <2e-16 ***
ORIGIN_SZ1272      12.1395848  0.1098244   110.54   <2e-16 ***
ORIGIN_SZ1273      14.7587325  0.0214139   689.21   <2e-16 ***
ORIGIN_SZ1277      16.2461192  0.0083460  1946.58   <2e-16 ***
ORIGIN_SZ1278      14.6103330  0.0199997   730.53   <2e-16 ***
ORIGIN_SZ128       16.3527808  0.0300670   543.88   <2e-16 ***
ORIGIN_SZ1283      16.3843652  0.0067056  2443.37   <2e-16 ***
ORIGIN_SZ1284      15.4393080  0.0087339  1767.75   <2e-16 ***
ORIGIN_SZ1285      15.9586004  0.0068919  2315.56   <2e-16 ***
ORIGIN_SZ1286      14.5900822  0.0161669   902.47   <2e-16 ***
ORIGIN_SZ1289      13.7718026  0.0386504   356.32   <2e-16 ***
ORIGIN_SZ129       15.4949105  0.1796524    86.25   <2e-16 ***
ORIGIN_SZ1293      13.3887163  0.0754731   177.40   <2e-16 ***
ORIGIN_SZ1294      15.6526167  0.0139965  1118.32   <2e-16 ***
ORIGIN_SZ1295      14.4342720  0.0259119   557.05   <2e-16 ***
ORIGIN_SZ1298      15.0564686  0.0147162  1023.12   <2e-16 ***
ORIGIN_SZ1299      15.9098023  0.0123491  1288.33   <2e-16 ***
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ORIGIN_SZ512       16.7016448  0.0074002  2256.92   <2e-16 ***
ORIGIN_SZ513       13.9351395  0.0535635   260.16   <2e-16 ***
ORIGIN_SZ514       15.2485695  0.0460428   331.18   <2e-16 ***
ORIGIN_SZ515       13.1282593  0.1072702   122.39   <2e-16 ***
ORIGIN_SZ530       13.8360158  0.0776919   178.09   <2e-16 ***
ORIGIN_SZ531       14.1162609  0.0355623   396.94   <2e-16 ***
ORIGIN_SZ532       14.0807693  0.0297327   473.58   <2e-16 ***
ORIGIN_SZ533       16.5002963  0.0072763  2267.68   <2e-16 ***
ORIGIN_SZ534       16.7888616  0.0080552  2084.24   <2e-16 ***
ORIGIN_SZ536       14.3743013  0.0426776   336.81   <2e-16 ***
ORIGIN_SZ537       13.1919762  0.1581631    83.41   <2e-16 ***
ORIGIN_SZ538       12.2824778  0.2085465    58.90   <2e-16 ***
ORIGIN_SZ551       13.2622297  0.0822648   161.21   <2e-16 ***
ORIGIN_SZ552       14.6075783  0.0537895   271.57   <2e-16 ***
ORIGIN_SZ553       13.9638465  0.0280110   498.51   <2e-16 ***
ORIGIN_SZ554       16.3204416  0.0083981  1943.34   <2e-16 ***
ORIGIN_SZ555       15.9094978  0.0177841   894.59   <2e-16 ***
ORIGIN_SZ559       14.7651005  0.0772609   191.11   <2e-16 ***
ORIGIN_SZ560       14.1140930  0.0913689   154.47   <2e-16 ***
ORIGIN_SZ572       13.3018206  0.1491159    89.20   <2e-16 ***
ORIGIN_SZ573       14.0285031  0.0482790   290.57   <2e-16 ***
ORIGIN_SZ574       14.4904620  0.0828401   174.92   <2e-16 ***
ORIGIN_SZ575       17.5871177  0.0048019  3662.53   <2e-16 ***
ORIGIN_SZ576       15.9635448  0.0103235  1546.33   <2e-16 ***
ORIGIN_SZ578       12.0461263  0.2041613    59.00   <2e-16 ***
ORIGIN_SZ582       14.1203440  0.1155493   122.20   <2e-16 ***
ORIGIN_SZ583       14.3728774  0.1260631   114.01   <2e-16 ***
ORIGIN_SZ584       15.3376719  0.0744587   205.99   <2e-16 ***
ORIGIN_SZ593       12.9259743  0.1104962   116.98   <2e-16 ***
ORIGIN_SZ594       14.2281380  0.0486870   292.24   <2e-16 ***
ORIGIN_SZ595       14.2869290  0.0233635   611.51   <2e-16 ***
ORIGIN_SZ596       15.8038066  0.0095509  1654.69   <2e-16 ***
ORIGIN_SZ597       13.3901187  0.0967348   138.42   <2e-16 ***
ORIGIN_SZ603       13.6909970  0.1349036   101.49   <2e-16 ***
ORIGIN_SZ604       13.9170728  0.1429232    97.38   <2e-16 ***
ORIGIN_SZ615       12.9955912  0.0732112   177.51   <2e-16 ***
ORIGIN_SZ616       14.1429713  0.0377902   374.25   <2e-16 ***
ORIGIN_SZ617       13.5217843  0.0367943   367.50   <2e-16 ***
ORIGIN_SZ618       16.4353410  0.0078774  2086.40   <2e-16 ***
ORIGIN_SZ620       13.3624232  0.0772378   173.00   <2e-16 ***
ORIGIN_SZ637       13.6521076  0.0446248   305.93   <2e-16 ***
ORIGIN_SZ638       16.1252374  0.0078854  2044.96   <2e-16 ***
ORIGIN_SZ657       14.3060394  0.0281441   508.31   <2e-16 ***
ORIGIN_SZ658       14.9142185  0.0149680   996.41   <2e-16 ***
ORIGIN_SZ659       15.6258314  0.0111233  1404.78   <2e-16 ***
ORIGIN_SZ66        12.9051660  0.2182414    59.13   <2e-16 ***
ORIGIN_SZ660       16.8826536  0.0060620  2785.01   <2e-16 ***
ORIGIN_SZ662       16.8308947  0.0119397  1409.66   <2e-16 ***
ORIGIN_SZ67        14.9161098  0.0430515   346.47   <2e-16 ***
ORIGIN_SZ677       14.7507825  0.0319092   462.27   <2e-16 ***
ORIGIN_SZ678       12.8503225  0.0638541   201.25   <2e-16 ***
ORIGIN_SZ679       16.3448053  0.0075625  2161.29   <2e-16 ***
ORIGIN_SZ68        13.2821642  0.1491137    89.07   <2e-16 ***
ORIGIN_SZ680       16.4599230  0.0069986  2351.90   <2e-16 ***
ORIGIN_SZ681       15.0994423  0.0196881   766.93   <2e-16 ***
ORIGIN_SZ699       14.6398338  0.0268190   545.88   <2e-16 ***
ORIGIN_SZ700       15.7398605  0.0107838  1459.59   <2e-16 ***
ORIGIN_SZ701       15.3417544  0.0142152  1079.25   <2e-16 ***
ORIGIN_SZ702       16.4868986  0.0068970  2390.44   <2e-16 ***
ORIGIN_SZ704       14.1503712  0.0440859   320.97   <2e-16 ***
ORIGIN_SZ722       14.1341716  0.0267479   528.42   <2e-16 ***
ORIGIN_SZ725       13.9151547  0.0449960   309.25   <2e-16 ***
ORIGIN_SZ730       14.0915733  0.0874391   161.16   <2e-16 ***
ORIGIN_SZ741       14.1020706  0.0310995   453.45   <2e-16 ***
ORIGIN_SZ743       13.6885325  0.0269887   507.19   <2e-16 ***
ORIGIN_SZ744       15.9477941  0.0087753  1817.35   <2e-16 ***
ORIGIN_SZ752       15.2402852  0.0408741   372.86   <2e-16 ***
ORIGIN_SZ761       14.8233801  0.0297395   498.44   <2e-16 ***
ORIGIN_SZ762       15.5528676  0.0142525  1091.23   <2e-16 ***
ORIGIN_SZ763       13.0080070  0.0392052   331.79   <2e-16 ***
ORIGIN_SZ764       16.4785933  0.0064257  2564.49   <2e-16 ***
ORIGIN_SZ765       15.4073627  0.0169338   909.86   <2e-16 ***
ORIGIN_SZ767       16.7366919  0.0085045  1967.99   <2e-16 ***
ORIGIN_SZ772       14.6249639  0.0352485   414.91   <2e-16 ***
ORIGIN_SZ784       12.8480848  0.0421405   304.89   <2e-16 ***
ORIGIN_SZ785       15.4205593  0.0091684  1681.92   <2e-16 ***
ORIGIN_SZ786       14.9527097  0.0128413  1164.42   <2e-16 ***
ORIGIN_SZ787       15.6979536  0.0153747  1021.03   <2e-16 ***
ORIGIN_SZ788       15.9864508  0.0121222  1318.77   <2e-16 ***
ORIGIN_SZ789       14.8668443  0.0215851   688.76   <2e-16 ***
ORIGIN_SZ803       13.3590303  0.0657540   203.17   <2e-16 ***
ORIGIN_SZ804       16.0932880  0.0092255  1744.44   <2e-16 ***
ORIGIN_SZ805       16.2961923  0.0065380  2492.53   <2e-16 ***
ORIGIN_SZ806       15.6037348  0.0091400  1707.19   <2e-16 ***
ORIGIN_SZ807       16.3273741  0.0092199  1770.89   <2e-16 ***
ORIGIN_SZ808       14.4740781  0.0267782   540.52   <2e-16 ***
ORIGIN_SZ809       16.4075823  0.0074458  2203.61   <2e-16 ***
ORIGIN_SZ810       15.8883110  0.0116562  1363.08   <2e-16 ***
ORIGIN_SZ814       14.1929489  0.0359235   395.09   <2e-16 ***
ORIGIN_SZ819       19.2478029  0.0209043   920.76   <2e-16 ***
ORIGIN_SZ824       14.0317144  0.0449068   312.46   <2e-16 ***
ORIGIN_SZ826       13.6199962  0.0246473   552.60   <2e-16 ***
ORIGIN_SZ827       15.7632573  0.0085379  1846.26   <2e-16 ***
ORIGIN_SZ828       15.9961088  0.0076495  2091.14   <2e-16 ***
ORIGIN_SZ829       15.8314943  0.0103291  1532.70   <2e-16 ***
ORIGIN_SZ830       15.7037728  0.0121842  1288.86   <2e-16 ***
ORIGIN_SZ831       17.2914251  0.0053618  3224.94   <2e-16 ***
ORIGIN_SZ832       17.0908673  0.0076564  2232.24   <2e-16 ***
ORIGIN_SZ835       12.6563897  0.0781606   161.93   <2e-16 ***
ORIGIN_SZ844       13.2891553  0.0902493   147.25   <2e-16 ***
ORIGIN_SZ846       15.4067629  0.0107012  1439.73   <2e-16 ***
ORIGIN_SZ847       15.4831566  0.0103701  1493.06   <2e-16 ***
ORIGIN_SZ848       15.3398783  0.0100190  1531.07   <2e-16 ***
ORIGIN_SZ849       14.7055262  0.0156573   939.21   <2e-16 ***
ORIGIN_SZ850       15.9657454  0.0091534  1744.25   <2e-16 ***
ORIGIN_SZ851       16.0197286  0.0081614  1962.86   <2e-16 ***
ORIGIN_SZ852       15.6370301  0.0115122  1358.30   <2e-16 ***
ORIGIN_SZ853       17.3341786  0.0079670  2175.75   <2e-16 ***
ORIGIN_SZ854       13.1196325  0.0639792   205.06   <2e-16 ***
ORIGIN_SZ855       12.8355137  0.0839885   152.82   <2e-16 ***
ORIGIN_SZ856       14.8511248  0.0325038   456.90   <2e-16 ***
ORIGIN_SZ86        14.3406354  0.0731842   195.95   <2e-16 ***
ORIGIN_SZ866       14.8522028  0.0301767   492.17   <2e-16 ***
ORIGIN_SZ867       14.6319132  0.0183695   796.53   <2e-16 ***
ORIGIN_SZ868       14.9117376  0.0172067   866.62   <2e-16 ***
ORIGIN_SZ869       15.6249996  0.0134786  1159.25   <2e-16 ***
ORIGIN_SZ87        15.7462572  0.1213363   129.77   <2e-16 ***
ORIGIN_SZ870       16.5849505  0.0058749  2822.99   <2e-16 ***
ORIGIN_SZ871       16.6842482  0.0089680  1860.42   <2e-16 ***
ORIGIN_SZ872       14.0874653  0.0219645   641.38   <2e-16 ***
ORIGIN_SZ873       14.5880333  0.0179050   814.75   <2e-16 ***
ORIGIN_SZ874       14.6732896  0.0184909   793.54   <2e-16 ***
ORIGIN_SZ875       12.5693638  0.0976539   128.71   <2e-16 ***
ORIGIN_SZ876       12.4603236  0.0822715   151.45   <2e-16 ***
ORIGIN_SZ877       14.6926381  0.0290314   506.10   <2e-16 ***
ORIGIN_SZ88        15.8997807  0.0231652   686.37   <2e-16 ***
ORIGIN_SZ887       14.1377979  0.0233994   604.20   <2e-16 ***
ORIGIN_SZ888       14.9668033  0.0155085   965.07   <2e-16 ***
ORIGIN_SZ889       12.6517437  0.0534942   236.51   <2e-16 ***
ORIGIN_SZ89        12.2938875  0.1796375    68.44   <2e-16 ***
ORIGIN_SZ890       15.9525403  0.0078114  2042.21   <2e-16 ***
ORIGIN_SZ891       15.0765504  0.0219579   686.61   <2e-16 ***
ORIGIN_SZ893       16.1706351  0.0076046  2126.42   <2e-16 ***
ORIGIN_SZ894       13.8640928  0.0255834   541.92   <2e-16 ***
ORIGIN_SZ895       13.9650201  0.0281490   496.11   <2e-16 ***
ORIGIN_SZ896       13.0334530  0.0610771   213.39   <2e-16 ***
ORIGIN_SZ897       13.2146530  0.0673556   196.19   <2e-16 ***
ORIGIN_SZ898       14.1888920  0.0408014   347.75   <2e-16 ***
ORIGIN_SZ90        14.5607795  0.1005725   144.78   <2e-16 ***
ORIGIN_SZ908       14.6561646  0.0266372   550.22   <2e-16 ***
ORIGIN_SZ909       15.3104347  0.0109801  1394.38   <2e-16 ***
ORIGIN_SZ910       12.3102039  0.0574673   214.21   <2e-16 ***
ORIGIN_SZ911       15.1414435  0.0129015  1173.62   <2e-16 ***
ORIGIN_SZ912       15.8428381  0.0082539  1919.43   <2e-16 ***
ORIGIN_SZ915       15.7858628  0.0089398  1765.79   <2e-16 ***
ORIGIN_SZ917       15.9485266  0.0117520  1357.09   <2e-16 ***
ORIGIN_SZ918       13.6174307  0.0444290   306.50   <2e-16 ***
ORIGIN_SZ919       14.5143344  0.0263129   551.61   <2e-16 ***
ORIGIN_SZ928       14.4974164  0.0227624   636.90   <2e-16 ***
ORIGIN_SZ929       15.4744702  0.0096318  1606.60   <2e-16 ***
ORIGIN_SZ930       16.4730396  0.0060235  2734.79   <2e-16 ***
ORIGIN_SZ931       13.0005491  0.0420049   309.50   <2e-16 ***
ORIGIN_SZ932       13.4212779  0.0424873   315.89   <2e-16 ***
ORIGIN_SZ933       15.3897198  0.0122343  1257.92   <2e-16 ***
ORIGIN_SZ934       12.6362667  0.0463204   272.80   <2e-16 ***
ORIGIN_SZ935       17.2515974  0.0052986  3255.86   <2e-16 ***
ORIGIN_SZ938       11.8907810  0.1826057    65.12   <2e-16 ***
ORIGIN_SZ939       16.8705581  0.0073711  2288.75   <2e-16 ***
ORIGIN_SZ940       13.4575628  0.1222120   110.12   <2e-16 ***
ORIGIN_SZ949       14.6120242  0.0195090   748.99   <2e-16 ***
ORIGIN_SZ950       16.5723217  0.0076145  2176.41   <2e-16 ***
ORIGIN_SZ951       16.8093561  0.0055897  3007.22   <2e-16 ***
ORIGIN_SZ952       14.4268859  0.0314233   459.12   <2e-16 ***
ORIGIN_SZ953       14.5906109  0.0189809   768.70   <2e-16 ***
ORIGIN_SZ954       13.1917954  0.0331139   398.38   <2e-16 ***
ORIGIN_SZ955       15.7361311  0.0095658  1645.04   <2e-16 ***
ORIGIN_SZ956       13.8128917  0.0232756   593.45   <2e-16 ***
ORIGIN_SZ957       15.9686291  0.0100832  1583.69   <2e-16 ***
ORIGIN_SZ959       13.3442839  0.0684411   194.97   <2e-16 ***
ORIGIN_SZ961       13.5557445  0.0448593   302.18   <2e-16 ***
ORIGIN_SZ962       22.0953950  0.0060081  3677.58   <2e-16 ***
ORIGIN_SZ970       15.0577394  0.0130321  1155.44   <2e-16 ***
ORIGIN_SZ971       15.7903098  0.0078110  2021.55   <2e-16 ***
ORIGIN_SZ972       15.6663454  0.0094224  1662.67   <2e-16 ***
ORIGIN_SZ974       14.9416181  0.0146258  1021.59   <2e-16 ***
ORIGIN_SZ975       14.3062522  0.0198409   721.05   <2e-16 ***
ORIGIN_SZ976       14.3381365  0.0197690   725.28   <2e-16 ***
ORIGIN_SZ977       16.1289917  0.0076821  2099.55   <2e-16 ***
ORIGIN_SZ978       15.8699511  0.0135393  1172.14   <2e-16 ***
ORIGIN_SZ982       13.7058893  0.0335654   408.33   <2e-16 ***
ORIGIN_SZ983       17.8136822  0.0075354  2364.01   <2e-16 ***
ORIGIN_SZ984       19.7793698  0.0066796  2961.16   <2e-16 ***
ORIGIN_SZ991       15.1433400  0.0134885  1122.68   <2e-16 ***
ORIGIN_SZ992       15.3520267  0.0114321  1342.88   <2e-16 ***
ORIGIN_SZ993       14.5899841  0.0152310   957.92   <2e-16 ***
ORIGIN_SZ994       14.3168785  0.0185980   769.81   <2e-16 ***
ORIGIN_SZ995       15.8579526  0.0087774  1806.68   <2e-16 ***
ORIGIN_SZ996       14.8048932  0.0156119   948.31   <2e-16 ***
ORIGIN_SZ997       14.0468579  0.0437726   320.90   <2e-16 ***
ORIGIN_SZ998       16.2337342  0.0080936  2005.76   <2e-16 ***
ORIGIN_SZ999       16.3072010  0.0102976  1583.59   <2e-16 ***
log(SCHOOL_COUNT)   0.2593888  0.0012140   213.67   <2e-16 ***
log(ENTERTN_COUNT) -0.0559950  0.0012458   -44.95   <2e-16 ***
log(RTSS_COUNT)     0.7053466  0.0014582   483.72   <2e-16 ***
log(LR_COUNT)      -0.0186901  0.0006064   -30.82   <2e-16 ***
log(RETAILS_COUNT)  0.3041548  0.0002912  1044.38   <2e-16 ***
log(DIST)          -1.5020359  0.0004760 -3155.86   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 81537309  on 61828  degrees of freedom
Residual deviance:  9621538  on 61001  degrees of freedom
AIC: 9912398

Number of Fisher Scoring iterations: 7
CalcRSquared <- function(observed, estimated){
  r <- cor(observed, estimated)
  R2 <- r^2
  R2
}
CalcRSquared(orcSIM_Poisson$data$TRIPS, orcSIM_Poisson$fitted.values)
[1] 0.4426548

Conclusion of Origin_Constrained model

Currently, the OM model yields an R-squared value of 44%, indicating that the model explains approximately 44% of the variance in the response variable TRIPS. The significant p-values suggest that the model is effective, as these values indicate statistically significant impacts of the explanatory variables on the response variable. However, given that the fit is only 44%, it is necessary to explore comparisons with different models. This suggests that there might be unexplained variability, possibly due to important variables not included in the model or complex nonlinear relationships not captured by the current model. Therefore, further analysis is required to enhance the explanatory power of the model.

Doubly_Constrained model

dbcSIM_Poisson <- glm(formula = TRIPS ~ 
                ORIGIN_SZ + 
                DESTIN_SZ +
                log(DIST),
              family = poisson(link = "log"),
              data = inter_zonal_flow,
              na.action = na.exclude)
summary(dbcSIM_Poisson)

Call:
glm(formula = TRIPS ~ ORIGIN_SZ + DESTIN_SZ + log(DIST), family = poisson(link = "log"), 
    data = inter_zonal_flow, na.action = na.exclude)

Coefficients:
                Estimate Std. Error   z value Pr(>|z|)    
(Intercept)   13.0640549  0.0721898   180.968  < 2e-16 ***
ORIGIN_SZ1003  2.4306487  0.0490713    49.533  < 2e-16 ***
ORIGIN_SZ1004  2.4521733  0.0491255    49.917  < 2e-16 ***
ORIGIN_SZ1011 -0.0404507  0.0609743    -0.663 0.507070    
ORIGIN_SZ1012  0.9269684  0.0541662    17.113  < 2e-16 ***
ORIGIN_SZ1013  0.4939063  0.0524185     9.422  < 2e-16 ***
ORIGIN_SZ1014  0.5392816  0.0518772    10.395  < 2e-16 ***
ORIGIN_SZ1015 -0.1732128  0.0551950    -3.138 0.001700 ** 
ORIGIN_SZ1016  2.0935168  0.0493366    42.433  < 2e-16 ***
ORIGIN_SZ1018  1.1021795  0.0525039    20.992  < 2e-16 ***
ORIGIN_SZ1019  2.8326657  0.0491510    57.632  < 2e-16 ***
ORIGIN_SZ1023  0.9666893  0.0522211    18.511  < 2e-16 ***
ORIGIN_SZ1024  2.0741696  0.0493875    41.998  < 2e-16 ***
ORIGIN_SZ1025 -0.7800208  0.0724034   -10.773  < 2e-16 ***
ORIGIN_SZ1033  0.9135244  0.0515134    17.734  < 2e-16 ***
ORIGIN_SZ1034  1.4397837  0.0499966    28.798  < 2e-16 ***
ORIGIN_SZ1035  1.6289124  0.0497139    32.766  < 2e-16 ***
ORIGIN_SZ1036  1.6945172  0.0497184    34.082  < 2e-16 ***
ORIGIN_SZ1037  1.5688715  0.0495390    31.669  < 2e-16 ***
ORIGIN_SZ1043  1.6838454  0.0525854    32.021  < 2e-16 ***
ORIGIN_SZ1045  2.1033352  0.0491582    42.787  < 2e-16 ***
ORIGIN_SZ1046  2.0134750  0.0494993    40.677  < 2e-16 ***
ORIGIN_SZ1053  1.4843989  0.0503564    29.478  < 2e-16 ***
ORIGIN_SZ1054  0.6660582  0.0517640    12.867  < 2e-16 ***
ORIGIN_SZ1055  1.8741206  0.0494812    37.875  < 2e-16 ***
ORIGIN_SZ1056  0.9813962  0.0509245    19.272  < 2e-16 ***
ORIGIN_SZ1064 -0.7820504  0.1861739    -4.201 2.66e-05 ***
ORIGIN_SZ1066  2.1799422  0.0491284    44.372  < 2e-16 ***
ORIGIN_SZ1067  0.8369846  0.0531667    15.743  < 2e-16 ***
ORIGIN_SZ1074  1.3936197  0.0505324    27.579  < 2e-16 ***
ORIGIN_SZ1075 -0.4751740  0.0600533    -7.913 2.52e-15 ***
ORIGIN_SZ1076  0.7801192  0.0508528    15.341  < 2e-16 ***
ORIGIN_SZ1077  0.6373516  0.0520763    12.239  < 2e-16 ***
ORIGIN_SZ1079  1.6816491  0.0496877    33.844  < 2e-16 ***
ORIGIN_SZ1085 -1.9195106  0.1151501   -16.670  < 2e-16 ***
ORIGIN_SZ1087  1.1040121  0.0500637    22.052  < 2e-16 ***
ORIGIN_SZ1088 -0.1389263  0.0538845    -2.578 0.009931 ** 
ORIGIN_SZ109  -0.2204871  0.1161062    -1.899 0.057563 .  
ORIGIN_SZ1094 -0.8681177  0.0958703    -9.055  < 2e-16 ***
ORIGIN_SZ1095 -0.3178508  0.0724997    -4.384 1.16e-05 ***
ORIGIN_SZ1096  0.3740676  0.0707495     5.287 1.24e-07 ***
ORIGIN_SZ1097  2.3792386  0.0490412    48.515  < 2e-16 ***
ORIGIN_SZ1098 -0.0306528  0.0579699    -0.529 0.596964    
ORIGIN_SZ1099  1.4345640  0.0499274    28.733  < 2e-16 ***
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ORIGIN_SZ111   4.5907097  0.0527038    87.104  < 2e-16 ***
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ORIGIN_SZ1236  1.2469919  0.0527064    23.659  < 2e-16 ***
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ORIGIN_SZ1327  1.5665861  0.0492485    31.810  < 2e-16 ***
ORIGIN_SZ1328  0.8839024  0.0500116    17.674  < 2e-16 ***
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ORIGIN_SZ1333  0.6108447  0.0530453    11.516  < 2e-16 ***
ORIGIN_SZ1334  0.9964997  0.0522597    19.068  < 2e-16 ***
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ORIGIN_SZ1338 -2.1871734  0.0975331   -22.425  < 2e-16 ***
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ORIGIN_SZ1350  0.5488517  0.0532954    10.298  < 2e-16 ***
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ORIGIN_SZ1357 -0.5660007  0.0666995    -8.486  < 2e-16 ***
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ORIGIN_SZ1376  0.6819754  0.0540488    12.618  < 2e-16 ***
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ORIGIN_SZ1417  1.2373262  0.0496847    24.904  < 2e-16 ***
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ORIGIN_SZ1541  2.6780090  0.0494780    54.125  < 2e-16 ***
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ORIGIN_SZ1584  0.2978409  0.0520456     5.723 1.05e-08 ***
ORIGIN_SZ1585  1.8775174  0.0496322    37.829  < 2e-16 ***
ORIGIN_SZ1586  0.1431878  0.0532950     2.687 0.007216 ** 
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ORIGIN_SZ1603  2.0538368  0.0491007    41.829  < 2e-16 ***
ORIGIN_SZ1604  0.6845451  0.0503579    13.594  < 2e-16 ***
ORIGIN_SZ1605  1.8077443  0.0491381    36.789  < 2e-16 ***
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ORIGIN_SZ1630  1.1945882  0.0508096    23.511  < 2e-16 ***
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ORIGIN_SZ1644  0.0143722  0.0558374     0.257 0.796875    
ORIGIN_SZ1645  1.2967242  0.0497988    26.039  < 2e-16 ***
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ORIGIN_SZ1647  1.5551575  0.0492589    31.571  < 2e-16 ***
ORIGIN_SZ1648  1.6007164  0.0493586    32.430  < 2e-16 ***
ORIGIN_SZ1649  2.1520886  0.0491561    43.781  < 2e-16 ***
ORIGIN_SZ1650  2.1747717  0.0495686    43.874  < 2e-16 ***
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ORIGIN_SZ1665  2.1087353  0.0489962    43.039  < 2e-16 ***
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ORIGIN_SZ1667  1.5762010  0.0515925    30.551  < 2e-16 ***
ORIGIN_SZ1668  1.5944366  0.0493531    32.307  < 2e-16 ***
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ORIGIN_SZ1671  2.5545744  0.0497733    51.324  < 2e-16 ***
ORIGIN_SZ1672  1.7846061  0.0501811    35.563  < 2e-16 ***
ORIGIN_SZ1684  0.8807424  0.0532033    16.554  < 2e-16 ***
ORIGIN_SZ1685  1.5778451  0.0493925    31.945  < 2e-16 ***
ORIGIN_SZ1686  1.5906468  0.0493775    32.214  < 2e-16 ***
ORIGIN_SZ1687  1.3002295  0.0507304    25.630  < 2e-16 ***
ORIGIN_SZ1688  0.9712387  0.0501455    19.368  < 2e-16 ***
ORIGIN_SZ1689  0.3824819  0.0515754     7.416 1.21e-13 ***
ORIGIN_SZ1690  0.7614098  0.0508503    14.974  < 2e-16 ***
ORIGIN_SZ1691  1.7619016  0.0493256    35.720  < 2e-16 ***
ORIGIN_SZ1692  1.1237446  0.0513772    21.872  < 2e-16 ***
ORIGIN_SZ1706  1.4978325  0.0498063    30.073  < 2e-16 ***
ORIGIN_SZ1707  1.3636494  0.0493820    27.614  < 2e-16 ***
ORIGIN_SZ1708  1.8383254  0.0492168    37.352  < 2e-16 ***
ORIGIN_SZ1709  1.1689418  0.0499835    23.387  < 2e-16 ***
ORIGIN_SZ1710  1.9425579  0.0492827    39.417  < 2e-16 ***
ORIGIN_SZ1711  2.6807121  0.0489385    54.777  < 2e-16 ***
ORIGIN_SZ1712  2.4380827  0.0489105    49.848  < 2e-16 ***
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ORIGIN_SZ1714  2.3617287  0.0492839    47.921  < 2e-16 ***
ORIGIN_SZ172   1.2355483  0.1093586    11.298  < 2e-16 ***
ORIGIN_SZ1726 -2.5597188  0.5023692    -5.095 3.48e-07 ***
ORIGIN_SZ1727  1.4439792  0.0495777    29.126  < 2e-16 ***
ORIGIN_SZ1728  2.1528713  0.0490201    43.918  < 2e-16 ***
ORIGIN_SZ1729  1.2203259  0.0497557    24.526  < 2e-16 ***
ORIGIN_SZ1730 -0.2972514  0.0576936    -5.152 2.57e-07 ***
ORIGIN_SZ1731  1.7204587  0.0493915    34.833  < 2e-16 ***
ORIGIN_SZ1732  1.9385250  0.0490699    39.505  < 2e-16 ***
ORIGIN_SZ1733  1.4721862  0.0494004    29.801  < 2e-16 ***
ORIGIN_SZ1734  1.7717114  0.0493137    35.927  < 2e-16 ***
ORIGIN_SZ1735  2.7262634  0.0506269    53.850  < 2e-16 ***
ORIGIN_SZ174  -0.1848138  0.0976136    -1.893 0.058315 .  
ORIGIN_SZ1748  0.8221629  0.0505108    16.277  < 2e-16 ***
ORIGIN_SZ1749  2.3433215  0.0489270    47.894  < 2e-16 ***
ORIGIN_SZ175  -0.2718457  0.0835248    -3.255 0.001135 ** 
ORIGIN_SZ1750  1.0463463  0.0497760    21.021  < 2e-16 ***
ORIGIN_SZ1751  0.2128327  0.0531366     4.005 6.19e-05 ***
ORIGIN_SZ1753  1.9803548  0.0491729    40.273  < 2e-16 ***
ORIGIN_SZ1754  2.8003056  0.0488337    57.344  < 2e-16 ***
ORIGIN_SZ1755  1.9039006  0.0491471    38.739  < 2e-16 ***
ORIGIN_SZ1756  1.5384568  0.0495489    31.049  < 2e-16 ***
ORIGIN_SZ1757 -1.1861698  0.0806269   -14.712  < 2e-16 ***
ORIGIN_SZ176   1.2881236  0.0551646    23.351  < 2e-16 ***
ORIGIN_SZ1768 -1.8602842  0.1538047   -12.095  < 2e-16 ***
ORIGIN_SZ1769  1.1769081  0.0496627    23.698  < 2e-16 ***
ORIGIN_SZ1770  2.1418117  0.0495165    43.254  < 2e-16 ***
ORIGIN_SZ1771  0.6141314  0.0512947    11.973  < 2e-16 ***
ORIGIN_SZ1772  1.0346047  0.0582529    17.761  < 2e-16 ***
ORIGIN_SZ1774  1.7653763  0.0492355    35.856  < 2e-16 ***
ORIGIN_SZ1775  1.2743190  0.0496498    25.666  < 2e-16 ***
ORIGIN_SZ1776  2.9688842  0.0488280    60.803  < 2e-16 ***
ORIGIN_SZ1777  1.8738955  0.0494189    37.919  < 2e-16 ***
ORIGIN_SZ1778  1.5479627  0.0537073    28.822  < 2e-16 ***
ORIGIN_SZ1790  2.3253584  0.0490627    47.396  < 2e-16 ***
ORIGIN_SZ1791  2.0126721  0.0492056    40.903  < 2e-16 ***
ORIGIN_SZ1792  1.3681296  0.0501662    27.272  < 2e-16 ***
ORIGIN_SZ1793  0.8955938  0.0508880    17.599  < 2e-16 ***
ORIGIN_SZ1794  0.3274535  0.0778696     4.205 2.61e-05 ***
ORIGIN_SZ1795 -1.4462054  0.0788270   -18.347  < 2e-16 ***
ORIGIN_SZ1796  1.9623351  0.0492748    39.824  < 2e-16 ***
ORIGIN_SZ1797  1.9592992  0.0491471    39.866  < 2e-16 ***
ORIGIN_SZ1798  1.7992687  0.0492362    36.544  < 2e-16 ***
ORIGIN_SZ1799  0.8601011  0.0512549    16.781  < 2e-16 ***
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ORIGIN_SZ1811  1.4505723  0.0495607    29.269  < 2e-16 ***
ORIGIN_SZ1812  2.4477902  0.0488961    50.061  < 2e-16 ***
ORIGIN_SZ1813  1.8744331  0.0491984    38.100  < 2e-16 ***
ORIGIN_SZ1817  1.5877205  0.0498318    31.862  < 2e-16 ***
ORIGIN_SZ1818  1.7246188  0.0492982    34.983  < 2e-16 ***
ORIGIN_SZ1819  2.8949333  0.0488900    59.213  < 2e-16 ***
ORIGIN_SZ1820 -0.4017580  0.0680551    -5.903 3.56e-09 ***
ORIGIN_SZ1832  2.7676793  0.0489267    56.568  < 2e-16 ***
ORIGIN_SZ1833  1.2638903  0.0496375    25.462  < 2e-16 ***
ORIGIN_SZ1834  1.3056083  0.0495783    26.334  < 2e-16 ***
ORIGIN_SZ1835  0.6127182  0.0513626    11.929  < 2e-16 ***
ORIGIN_SZ1837 -0.2056854  0.1140862    -1.803 0.071405 .  
ORIGIN_SZ1839  1.4175355  0.0501331    28.275  < 2e-16 ***
ORIGIN_SZ1840  2.8386639  0.0488850    58.068  < 2e-16 ***
ORIGIN_SZ1841  0.4595002  0.0555996     8.264  < 2e-16 ***
ORIGIN_SZ1842  3.0801118  0.0516651    59.617  < 2e-16 ***
ORIGIN_SZ1853  1.4230314  0.0494450    28.780  < 2e-16 ***
ORIGIN_SZ1854  1.7929696  0.0492756    36.387  < 2e-16 ***
ORIGIN_SZ1855  1.9432353  0.0492950    39.421  < 2e-16 ***
ORIGIN_SZ1858  0.4870561  0.0627208     7.765 8.14e-15 ***
ORIGIN_SZ1860  2.2641012  0.0515419    43.927  < 2e-16 ***
ORIGIN_SZ1861  1.8016622  0.0494782    36.413  < 2e-16 ***
ORIGIN_SZ1874  1.6512681  0.0497583    33.186  < 2e-16 ***
ORIGIN_SZ1875 -0.0925672  0.0547564    -1.691 0.090927 .  
ORIGIN_SZ1876  1.9788833  0.0533927    37.063  < 2e-16 ***
ORIGIN_SZ1877  1.6160728  0.0495138    32.639  < 2e-16 ***
ORIGIN_SZ1880 -0.5107140  0.0865799    -5.899 3.66e-09 ***
ORIGIN_SZ1882  1.9094532  0.0494756    38.594  < 2e-16 ***
ORIGIN_SZ1883  1.6865738  0.0525723    32.081  < 2e-16 ***
ORIGIN_SZ1895  1.7023263  0.0493844    34.471  < 2e-16 ***
ORIGIN_SZ1896  1.0683985  0.0499770    21.378  < 2e-16 ***
ORIGIN_SZ1897  1.0858318  0.0505515    21.480  < 2e-16 ***
ORIGIN_SZ1898 -2.0827558  0.1150873   -18.097  < 2e-16 ***
ORIGIN_SZ1901 -0.8914243  0.1044838    -8.532  < 2e-16 ***
ORIGIN_SZ1903  1.2137023  0.0522193    23.242  < 2e-16 ***
ORIGIN_SZ1916 -1.2364144  0.0861691   -14.349  < 2e-16 ***
ORIGIN_SZ1917  0.9184068  0.0504052    18.220  < 2e-16 ***
ORIGIN_SZ1918  1.7284905  0.0497301    34.757  < 2e-16 ***
ORIGIN_SZ1919  1.6862474  0.0494984    34.067  < 2e-16 ***
ORIGIN_SZ1922  0.0329627  0.0722954     0.456 0.648430    
ORIGIN_SZ1924  1.4452533  0.0520399    27.772  < 2e-16 ***
ORIGIN_SZ1937  1.3498380  0.0499793    27.008  < 2e-16 ***
ORIGIN_SZ1938  1.8156862  0.0491961    36.907  < 2e-16 ***
ORIGIN_SZ1939  1.9637745  0.0493515    39.792  < 2e-16 ***
ORIGIN_SZ1942 -0.4360185  0.0779902    -5.591 2.26e-08 ***
ORIGIN_SZ195   0.4766703  0.0810571     5.881 4.09e-09 ***
ORIGIN_SZ1958 -1.7154329  0.2020901    -8.488  < 2e-16 ***
ORIGIN_SZ1959  1.0060830  0.0505869    19.888  < 2e-16 ***
ORIGIN_SZ196  -0.2319756  0.0707800    -3.277 0.001048 ** 
ORIGIN_SZ1960  3.4547668  0.0487366    70.887  < 2e-16 ***
ORIGIN_SZ1961  1.0046818  0.0505037    19.893  < 2e-16 ***
ORIGIN_SZ1962  1.8291916  0.0494421    36.997  < 2e-16 ***
ORIGIN_SZ1964 -0.2290485  0.0807525    -2.836 0.004562 ** 
ORIGIN_SZ197  -1.0561746  0.1795484    -5.882 4.04e-09 ***
ORIGIN_SZ1979  1.1098002  0.0506262    21.921  < 2e-16 ***
ORIGIN_SZ1980 -0.7878692  0.0560384   -14.059  < 2e-16 ***
ORIGIN_SZ1981  1.4391043  0.0494287    29.115  < 2e-16 ***
ORIGIN_SZ1982  1.0125714  0.0522354    19.385  < 2e-16 ***
ORIGIN_SZ1983  1.8544032  0.0493964    37.541  < 2e-16 ***
ORIGIN_SZ1984  0.7100715  0.0511563    13.880  < 2e-16 ***
ORIGIN_SZ1985  1.0385696  0.0506672    20.498  < 2e-16 ***
ORIGIN_SZ2001  1.4539833  0.0497012    29.254  < 2e-16 ***
ORIGIN_SZ2002  1.8202086  0.0491043    37.068  < 2e-16 ***
ORIGIN_SZ2003  1.7524529  0.0493239    35.529  < 2e-16 ***
ORIGIN_SZ2004  2.4389760  0.0490575    49.717  < 2e-16 ***
ORIGIN_SZ2005  1.7732699  0.0493824    35.909  < 2e-16 ***
ORIGIN_SZ2006  1.2292148  0.0502485    24.463  < 2e-16 ***
ORIGIN_SZ2007 -0.3106531  0.0615652    -5.046 4.51e-07 ***
ORIGIN_SZ2022  1.9297470  0.0496412    38.874  < 2e-16 ***
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ORIGIN_SZ2024  1.6956047  0.0492533    34.426  < 2e-16 ***
ORIGIN_SZ2025  1.2769329  0.0494904    25.802  < 2e-16 ***
ORIGIN_SZ2026 -0.0296230  0.0539021    -0.550 0.582614    
ORIGIN_SZ2027  2.2240114  0.0492002    45.203  < 2e-16 ***
ORIGIN_SZ2043  1.1367553  0.0505806    22.474  < 2e-16 ***
ORIGIN_SZ2044  1.6134591  0.0493553    32.691  < 2e-16 ***
ORIGIN_SZ2045 -0.9483736  0.0944237   -10.044  < 2e-16 ***
ORIGIN_SZ2046  2.1612934  0.0489480    44.155  < 2e-16 ***
ORIGIN_SZ2047  1.2194295  0.0497829    24.495  < 2e-16 ***
ORIGIN_SZ2048  1.5186376  0.0495032    30.678  < 2e-16 ***
ORIGIN_SZ2049  0.5814792  0.0560634    10.372  < 2e-16 ***
ORIGIN_SZ2064  1.6505073  0.0495939    33.280  < 2e-16 ***
ORIGIN_SZ2065  0.7595061  0.0505254    15.032  < 2e-16 ***
ORIGIN_SZ2066  0.1131691  0.0589556     1.920 0.054913 .  
ORIGIN_SZ2067  3.3957652  0.0487488    69.658  < 2e-16 ***
ORIGIN_SZ2068  1.0571465  0.0507914    20.814  < 2e-16 ***
ORIGIN_SZ2069  1.6352794  0.0496300    32.949  < 2e-16 ***
ORIGIN_SZ2085  0.7202811  0.0516528    13.945  < 2e-16 ***
ORIGIN_SZ2086  1.9938654  0.0492821    40.458  < 2e-16 ***
ORIGIN_SZ2087  1.1780046  0.0499732    23.573  < 2e-16 ***
ORIGIN_SZ2088  1.5803103  0.0492100    32.114  < 2e-16 ***
ORIGIN_SZ2089  0.9452998  0.0502465    18.813  < 2e-16 ***
ORIGIN_SZ2090  2.9025919  0.0488709    59.393  < 2e-16 ***
ORIGIN_SZ2091 -0.6477150  0.0775141    -8.356  < 2e-16 ***
ORIGIN_SZ2105  0.1510249  0.0910426     1.659 0.097148 .  
ORIGIN_SZ2106 -0.4562448  0.0570038    -8.004 1.21e-15 ***
ORIGIN_SZ2107  0.6699059  0.0507688    13.195  < 2e-16 ***
ORIGIN_SZ2108  1.8785100  0.0493681    38.051  < 2e-16 ***
ORIGIN_SZ2109  1.3227553  0.0494133    26.769  < 2e-16 ***
ORIGIN_SZ2110  0.6032700  0.0510121    11.826  < 2e-16 ***
ORIGIN_SZ2111 -2.2379071  0.1108220   -20.194  < 2e-16 ***
ORIGIN_SZ2128  0.6026393  0.0530826    11.353  < 2e-16 ***
ORIGIN_SZ2129  0.2252338  0.0525483     4.286 1.82e-05 ***
ORIGIN_SZ2130  2.0653773  0.0490543    42.104  < 2e-16 ***
ORIGIN_SZ2131  2.1426674  0.0493450    43.422  < 2e-16 ***
ORIGIN_SZ2132  1.5287971  0.0495685    30.842  < 2e-16 ***
ORIGIN_SZ2148  1.5171068  0.0514238    29.502  < 2e-16 ***
ORIGIN_SZ2149 -0.7901734  0.0604572   -13.070  < 2e-16 ***
ORIGIN_SZ215   1.1087930  0.0806670    13.745  < 2e-16 ***
ORIGIN_SZ2150  1.8225699  0.0494456    36.860  < 2e-16 ***
ORIGIN_SZ2151  2.2172261  0.0490167    45.234  < 2e-16 ***
ORIGIN_SZ2152  2.3665441  0.0490633    48.234  < 2e-16 ***
ORIGIN_SZ2153  1.6945503  0.0499076    33.954  < 2e-16 ***
ORIGIN_SZ216   1.2089823  0.0652916    18.517  < 2e-16 ***
ORIGIN_SZ217   0.8183597  0.0595780    13.736  < 2e-16 ***
ORIGIN_SZ2171  1.1977518  0.0502918    23.816  < 2e-16 ***
ORIGIN_SZ2172  0.8281349  0.0510325    16.228  < 2e-16 ***
ORIGIN_SZ2173  1.1653832  0.0497808    23.410  < 2e-16 ***
ORIGIN_SZ2174  1.5977217  0.0497747    32.099  < 2e-16 ***
ORIGIN_SZ2191  0.7815993  0.0530175    14.742  < 2e-16 ***
ORIGIN_SZ2192  0.4426165  0.0527706     8.388  < 2e-16 ***
ORIGIN_SZ2193  1.1419448  0.0503275    22.690  < 2e-16 ***
ORIGIN_SZ2194  1.7462535  0.0494400    35.321  < 2e-16 ***
ORIGIN_SZ2195  0.4464232  0.0641484     6.959 3.42e-12 ***
ORIGIN_SZ2212 -0.3190137  0.0859418    -3.712 0.000206 ***
ORIGIN_SZ2213 -1.0236485  0.0770667   -13.283  < 2e-16 ***
ORIGIN_SZ2214  0.4009866  0.0592968     6.762 1.36e-11 ***
ORIGIN_SZ2215  1.4383567  0.0503873    28.546  < 2e-16 ***
ORIGIN_SZ2216  0.3845513  0.0535829     7.177 7.14e-13 ***
ORIGIN_SZ2233  0.1871952  0.0658346     2.843 0.004463 ** 
ORIGIN_SZ2234  0.8004626  0.0642377    12.461  < 2e-16 ***
ORIGIN_SZ2235  0.7157608  0.0547368    13.076  < 2e-16 ***
ORIGIN_SZ2236 -0.4825902  0.0616554    -7.827 4.99e-15 ***
ORIGIN_SZ2237 -0.4130691  0.0823079    -5.019 5.21e-07 ***
ORIGIN_SZ2256 -0.3352698  0.0763179    -4.393 1.12e-05 ***
ORIGIN_SZ2257  0.1027702  0.0610643     1.683 0.092378 .  
ORIGIN_SZ2258  0.1548679  0.0559721     2.767 0.005660 ** 
ORIGIN_SZ2259  0.3673617  0.0758250     4.845 1.27e-06 ***
ORIGIN_SZ2277 -0.1841639  0.0854358    -2.156 0.031116 *  
ORIGIN_SZ2278  0.1299589  0.0641497     2.026 0.042778 *  
ORIGIN_SZ2279 -0.0533265  0.0599053    -0.890 0.373369    
ORIGIN_SZ2280 -1.2483023  0.0945402   -13.204  < 2e-16 ***
ORIGIN_SZ2297  1.6863144  0.0517343    32.596  < 2e-16 ***
ORIGIN_SZ2300 -2.1474549  0.1618427   -13.269  < 2e-16 ***
ORIGIN_SZ2301 -0.4075584  0.0609377    -6.688 2.26e-11 ***
ORIGIN_SZ2318 -0.9154299  0.0695264   -13.167  < 2e-16 ***
ORIGIN_SZ2319  1.1398874  0.0505221    22.562  < 2e-16 ***
ORIGIN_SZ2322  2.6580429  0.0499715    53.191  < 2e-16 ***
ORIGIN_SZ2337  3.7351257  0.0518452    72.044  < 2e-16 ***
ORIGIN_SZ2341  1.9925326  0.0498987    39.932  < 2e-16 ***
ORIGIN_SZ2343  1.0303251  0.0523544    19.680  < 2e-16 ***
ORIGIN_SZ2361  1.0287347  0.0519501    19.802  < 2e-16 ***
ORIGIN_SZ2364  0.0553717  0.0683800     0.810 0.418076    
ORIGIN_SZ237   0.1277860  0.1481742     0.862 0.388465    
ORIGIN_SZ2379 -1.7705979  0.0973222   -18.193  < 2e-16 ***
ORIGIN_SZ238  -0.6164197  0.0982267    -6.275 3.49e-10 ***
ORIGIN_SZ2384  1.5455085  0.0538966    28.675  < 2e-16 ***
ORIGIN_SZ239  -0.8687048  0.1645593    -5.279 1.30e-07 ***
ORIGIN_SZ2405  1.3904428  0.0542131    25.648  < 2e-16 ***
ORIGIN_SZ2406  0.3400624  0.0680647     4.996 5.85e-07 ***
ORIGIN_SZ2426  1.3598716  0.0685814    19.829  < 2e-16 ***
ORIGIN_SZ2427  1.2708213  0.0564166    22.526  < 2e-16 ***
ORIGIN_SZ2505  0.5747920  0.0834291     6.890 5.60e-12 ***
ORIGIN_SZ257   1.7036294  0.0684887    24.875  < 2e-16 ***
ORIGIN_SZ258  -1.0918972  0.1009264   -10.819  < 2e-16 ***
ORIGIN_SZ259   0.0234666  0.0722855     0.325 0.745455    
ORIGIN_SZ278   3.3136572  0.0598490    55.367  < 2e-16 ***
ORIGIN_SZ279   1.1039544  0.0658049    16.776  < 2e-16 ***
ORIGIN_SZ280   0.2509118  0.0683852     3.669 0.000243 ***
ORIGIN_SZ298  -1.1287776  0.3570373    -3.162 0.001570 ** 
ORIGIN_SZ299   0.7004433  0.0899145     7.790 6.70e-15 ***
ORIGIN_SZ300   0.1746794  0.0747981     2.335 0.019525 *  
ORIGIN_SZ320   1.4047166  0.0780193    18.005  < 2e-16 ***
ORIGIN_SZ321   0.5187868  0.1060549     4.892 1.00e-06 ***
ORIGIN_SZ322  -0.2104098  0.0949952    -2.215 0.026763 *  
ORIGIN_SZ340   3.0323493  0.0620639    48.858  < 2e-16 ***
ORIGIN_SZ341   1.5946107  0.0682244    23.373  < 2e-16 ***
ORIGIN_SZ342   0.3964489  0.0739214     5.363 8.18e-08 ***
ORIGIN_SZ363   1.6339160  0.0653760    24.993  < 2e-16 ***
ORIGIN_SZ364  -0.0465762  0.0678981    -0.686 0.492731    
ORIGIN_SZ383   2.0657952  0.0608690    33.938  < 2e-16 ***
ORIGIN_SZ384  -0.2883858  0.0791373    -3.644 0.000268 ***
ORIGIN_SZ385  -1.8321972  0.1512748   -12.112  < 2e-16 ***
ORIGIN_SZ404   2.1542056  0.0688250    31.300  < 2e-16 ***
ORIGIN_SZ405   1.0422314  0.0710342    14.672  < 2e-16 ***
ORIGIN_SZ406   2.6724383  0.0498577    53.601  < 2e-16 ***
ORIGIN_SZ407   0.9846060  0.0581370    16.936  < 2e-16 ***
ORIGIN_SZ408   1.8480599  0.0521200    35.458  < 2e-16 ***
ORIGIN_SZ425  -0.2663169  0.1151959    -2.312 0.020785 *  
ORIGIN_SZ426   0.2887056  0.0680402     4.243 2.20e-05 ***
ORIGIN_SZ427  -0.1449570  0.0591900    -2.449 0.014325 *  
ORIGIN_SZ428   0.8357102  0.0566283    14.758  < 2e-16 ***
ORIGIN_SZ429   0.8354754  0.0573787    14.561  < 2e-16 ***
ORIGIN_SZ44   -1.9077556  0.2064853    -9.239  < 2e-16 ***
ORIGIN_SZ446   0.7591625  0.0789906     9.611  < 2e-16 ***
ORIGIN_SZ447  -0.7184651  0.0971515    -7.395 1.41e-13 ***
ORIGIN_SZ448  -0.6151542  0.0712329    -8.636  < 2e-16 ***
ORIGIN_SZ449   1.5866385  0.0507136    31.286  < 2e-16 ***
ORIGIN_SZ450   0.6753363  0.0541440    12.473  < 2e-16 ***
ORIGIN_SZ46    0.0149077  0.1038316     0.144 0.885836    
ORIGIN_SZ468   1.2138744  0.0608345    19.954  < 2e-16 ***
ORIGIN_SZ469  -0.3097769  0.0599255    -5.169 2.35e-07 ***
ORIGIN_SZ470   2.2693294  0.0495110    45.835  < 2e-16 ***
ORIGIN_SZ471   1.9694079  0.0522754    37.674  < 2e-16 ***
ORIGIN_SZ488   0.2049765  0.0900515     2.276 0.022833 *  
ORIGIN_SZ489  -2.4380626  0.2716738    -8.974  < 2e-16 ***
ORIGIN_SZ490   1.1060603  0.0535048    20.672  < 2e-16 ***
ORIGIN_SZ491   0.8267348  0.0511923    16.150  < 2e-16 ***
ORIGIN_SZ493  -2.4401800  0.2098685   -11.627  < 2e-16 ***
ORIGIN_SZ494   1.2669084  0.0599701    21.126  < 2e-16 ***
ORIGIN_SZ509   0.7074668  0.0690155    10.251  < 2e-16 ***
ORIGIN_SZ510   1.0268478  0.0570769    17.991  < 2e-16 ***
ORIGIN_SZ511  -0.0697666  0.0559312    -1.247 0.212263    
ORIGIN_SZ512   2.4475768  0.0491162    49.832  < 2e-16 ***
ORIGIN_SZ513  -0.5690416  0.0724316    -7.856 3.96e-15 ***
ORIGIN_SZ514   0.5588751  0.0669061     8.353  < 2e-16 ***
ORIGIN_SZ515  -0.5532178  0.1181041    -4.684 2.81e-06 ***
ORIGIN_SZ530   0.1992727  0.0920644     2.164 0.030427 *  
ORIGIN_SZ531   0.9619499  0.0605440    15.888  < 2e-16 ***
ORIGIN_SZ532   0.2629051  0.0569775     4.614 3.95e-06 ***
ORIGIN_SZ533   2.2722218  0.0490868    46.290  < 2e-16 ***
ORIGIN_SZ534   2.5321314  0.0492006    51.465  < 2e-16 ***
ORIGIN_SZ536   0.5091388  0.0648876     7.846 4.28e-15 ***
ORIGIN_SZ537  -1.0663925  0.1655347    -6.442 1.18e-10 ***
ORIGIN_SZ538  -1.6661192  0.2146829    -7.761 8.44e-15 ***
ORIGIN_SZ551  -0.3023224  0.0961191    -3.145 0.001659 ** 
ORIGIN_SZ552   0.1011391  0.0725397     1.394 0.163239    
ORIGIN_SZ553  -0.5301834  0.0560522    -9.459  < 2e-16 ***
ORIGIN_SZ554   1.7944560  0.0492664    36.424  < 2e-16 ***
ORIGIN_SZ555   1.4901238  0.0517085    28.818  < 2e-16 ***
ORIGIN_SZ559   0.4692962  0.0912409     5.143 2.70e-07 ***
ORIGIN_SZ560   0.2739061  0.1038874     2.637 0.008375 ** 
ORIGIN_SZ572  -0.9741404  0.1569090    -6.208 5.36e-10 ***
ORIGIN_SZ573   0.5436282  0.0689056     7.889 3.03e-15 ***
ORIGIN_SZ574   1.1232763  0.0966696    11.620  < 2e-16 ***
ORIGIN_SZ575   3.9411964  0.0487294    80.879  < 2e-16 ***
ORIGIN_SZ576   1.6960043  0.0496220    34.178  < 2e-16 ***
ORIGIN_SZ578  -2.6066088  0.2098795   -12.420  < 2e-16 ***
ORIGIN_SZ582  -0.0265457  0.1253000    -0.212 0.832219    
ORIGIN_SZ583   0.1824415  0.1350395     1.351 0.176688    
ORIGIN_SZ584   1.2821039  0.0888263    14.434  < 2e-16 ***
ORIGIN_SZ593  -0.7215244  0.1206909    -5.978 2.26e-09 ***
ORIGIN_SZ594   0.2442080  0.0688866     3.545 0.000393 ***
ORIGIN_SZ595   0.0314801  0.0538899     0.584 0.559115    
ORIGIN_SZ596   1.3667225  0.0494371    27.646  < 2e-16 ***
ORIGIN_SZ597  -1.0456896  0.1083244    -9.653  < 2e-16 ***
ORIGIN_SZ603  -0.3628031  0.1457189    -2.490 0.012783 *  
ORIGIN_SZ604  -0.2374258  0.1509075    -1.573 0.115645    
ORIGIN_SZ615  -0.8622917  0.0878927    -9.811  < 2e-16 ***
ORIGIN_SZ616  -0.0845604  0.0615341    -1.374 0.169378    
ORIGIN_SZ617  -1.0055094  0.0609173   -16.506  < 2e-16 ***
ORIGIN_SZ618   2.2284970  0.0491337    45.356  < 2e-16 ***
ORIGIN_SZ620  -1.2589433  0.0914458   -13.767  < 2e-16 ***
ORIGIN_SZ637  -0.6513854  0.0659606    -9.875  < 2e-16 ***
ORIGIN_SZ638   2.0140469  0.0491342    40.991  < 2e-16 ***
ORIGIN_SZ657   0.8395428  0.0561541    14.951  < 2e-16 ***
ORIGIN_SZ658   1.1203605  0.0507558    22.074  < 2e-16 ***
ORIGIN_SZ659   1.3967167  0.0497614    28.068  < 2e-16 ***
ORIGIN_SZ66    0.0157813  0.2412587     0.065 0.947846    
ORIGIN_SZ660   2.8765822  0.0488717    58.860  < 2e-16 ***
ORIGIN_SZ662   3.0645940  0.0499459    61.358  < 2e-16 ***
ORIGIN_SZ67    0.9609667  0.0699158    13.745  < 2e-16 ***
ORIGIN_SZ677   1.4422997  0.0582315    24.768  < 2e-16 ***
ORIGIN_SZ678  -1.0451327  0.0802133   -13.029  < 2e-16 ***
ORIGIN_SZ679   2.5500343  0.0490762    51.961  < 2e-16 ***
ORIGIN_SZ68   -1.5792138  0.1589689    -9.934  < 2e-16 ***
ORIGIN_SZ680   2.5769680  0.0490069    52.584  < 2e-16 ***
ORIGIN_SZ681   0.8865212  0.0523916    16.921  < 2e-16 ***
ORIGIN_SZ699   0.9211191  0.0555041    16.596  < 2e-16 ***
ORIGIN_SZ700   1.8748292  0.0496655    37.749  < 2e-16 ***
ORIGIN_SZ701   1.0915099  0.0505557    21.590  < 2e-16 ***
ORIGIN_SZ702   2.5069792  0.0489770    51.187  < 2e-16 ***
ORIGIN_SZ704  -0.3556378  0.0657481    -5.409 6.33e-08 ***
ORIGIN_SZ722  -0.1519476  0.0554122    -2.742 0.006104 ** 
ORIGIN_SZ725  -0.4161496  0.0662104    -6.285 3.27e-10 ***
ORIGIN_SZ730  -0.0655610  0.1020486    -0.642 0.520582    
ORIGIN_SZ741   0.5579370  0.0577258     9.665  < 2e-16 ***
ORIGIN_SZ743  -0.2945017  0.0554962    -5.307 1.12e-07 ***
ORIGIN_SZ744   1.9887461  0.0492605    40.372  < 2e-16 ***
ORIGIN_SZ752   1.2848514  0.0652970    19.677  < 2e-16 ***
ORIGIN_SZ761   1.0654056  0.0570600    18.672  < 2e-16 ***
ORIGIN_SZ762   1.6510146  0.0506142    32.620  < 2e-16 ***
ORIGIN_SZ763  -0.9986013  0.0623601   -16.013  < 2e-16 ***
ORIGIN_SZ764   2.7163023  0.0488917    55.558  < 2e-16 ***
ORIGIN_SZ765   1.1931176  0.0513826    23.220  < 2e-16 ***
ORIGIN_SZ767   2.6819707  0.0492278    54.481  < 2e-16 ***
ORIGIN_SZ772   1.1209842  0.0616258    18.190  < 2e-16 ***
ORIGIN_SZ784  -1.2025410  0.0642620   -18.713  < 2e-16 ***
ORIGIN_SZ785   1.5664541  0.0493309    31.754  < 2e-16 ***
ORIGIN_SZ786   0.9896101  0.0501459    19.735  < 2e-16 ***
ORIGIN_SZ787   1.5450001  0.0508883    30.361  < 2e-16 ***
ORIGIN_SZ788   1.8438639  0.0499959    36.880  < 2e-16 ***
ORIGIN_SZ789   0.5070248  0.0530991     9.549  < 2e-16 ***
ORIGIN_SZ803  -0.5945392  0.0817545    -7.272 3.54e-13 ***
ORIGIN_SZ804   2.4069464  0.0493684    48.755  < 2e-16 ***
ORIGIN_SZ805   2.6694113  0.0489052    54.583  < 2e-16 ***
ORIGIN_SZ806   1.7028675  0.0493265    34.522  < 2e-16 ***
ORIGIN_SZ807   2.4495610  0.0493843    49.602  < 2e-16 ***
ORIGIN_SZ808   0.5260196  0.0554078     9.494  < 2e-16 ***
ORIGIN_SZ809   2.3160240  0.0490269    47.240  < 2e-16 ***
ORIGIN_SZ810   1.5641298  0.0498934    31.349  < 2e-16 ***
ORIGIN_SZ814   0.9421254  0.0612773    15.375  < 2e-16 ***
ORIGIN_SZ819   2.3974667  0.0559046    42.885  < 2e-16 ***
ORIGIN_SZ824   0.3646356  0.0662390     5.505 3.69e-08 ***
ORIGIN_SZ826  -0.3534812  0.0543911    -6.499 8.09e-11 ***
ORIGIN_SZ827   1.8631308  0.0492329    37.843  < 2e-16 ***
ORIGIN_SZ828   2.1078160  0.0490647    42.960  < 2e-16 ***
ORIGIN_SZ829   1.8546381  0.0495720    37.413  < 2e-16 ***
ORIGIN_SZ830   1.6192722  0.0499945    32.389  < 2e-16 ***
ORIGIN_SZ831   3.4589025  0.0487213    70.994  < 2e-16 ***
ORIGIN_SZ832   2.8071430  0.0492101    57.044  < 2e-16 ***
ORIGIN_SZ835  -0.7498687  0.0924025    -8.115 4.85e-16 ***
ORIGIN_SZ844  -0.7864059  0.1024602    -7.675 1.65e-14 ***
ORIGIN_SZ846   1.6861912  0.0496438    33.966  < 2e-16 ***
ORIGIN_SZ847   1.6537378  0.0495766    33.357  < 2e-16 ***
ORIGIN_SZ848   1.4951970  0.0494963    30.208  < 2e-16 ***
ORIGIN_SZ849   0.5823333  0.0509558    11.428  < 2e-16 ***
ORIGIN_SZ850   1.9355393  0.0493246    39.241  < 2e-16 ***
ORIGIN_SZ851   2.0113029  0.0491331    40.936  < 2e-16 ***
ORIGIN_SZ852   1.4651061  0.0498570    29.386  < 2e-16 ***
ORIGIN_SZ853   3.2895141  0.0492655    66.771  < 2e-16 ***
ORIGIN_SZ854  -0.1158287  0.0803655    -1.441 0.149507    
ORIGIN_SZ855  -0.9065940  0.0971171    -9.335  < 2e-16 ***
ORIGIN_SZ856   1.1543453  0.0587598    19.645  < 2e-16 ***
ORIGIN_SZ86   -0.9868308  0.0973280   -10.139  < 2e-16 ***
ORIGIN_SZ866   1.0066866  0.0571806    17.605  < 2e-16 ***
ORIGIN_SZ867   0.7533821  0.0518525    14.529  < 2e-16 ***
ORIGIN_SZ868   0.8638732  0.0514383    16.794  < 2e-16 ***
ORIGIN_SZ869   2.0331093  0.0503843    40.352  < 2e-16 ***
ORIGIN_SZ87    1.5002095  0.1318262    11.380  < 2e-16 ***
ORIGIN_SZ870   2.8930829  0.0488090    59.274  < 2e-16 ***
ORIGIN_SZ871   2.7667302  0.0493668    56.044  < 2e-16 ***
ORIGIN_SZ872   0.1349613  0.0531888     2.537 0.011168 *  
ORIGIN_SZ873   0.5355640  0.0516619    10.367  < 2e-16 ***
ORIGIN_SZ874   0.3917353  0.0518701     7.552 4.28e-14 ***
ORIGIN_SZ875  -0.5954092  0.1090877    -5.458 4.81e-08 ***
ORIGIN_SZ876  -1.4033120  0.0955576   -14.686  < 2e-16 ***
ORIGIN_SZ877   1.0263154  0.0568459    18.054  < 2e-16 ***
ORIGIN_SZ88    2.0821410  0.0591353    35.210  < 2e-16 ***
ORIGIN_SZ887   0.4043641  0.0538946     7.503 6.24e-14 ***
ORIGIN_SZ888   0.9275887  0.0509022    18.223  < 2e-16 ***
ORIGIN_SZ889  -1.2034270  0.0722183   -16.664  < 2e-16 ***
ORIGIN_SZ89   -0.1918784  0.1884608    -1.018 0.308614    
ORIGIN_SZ890   2.2041581  0.0490861    44.904  < 2e-16 ***
ORIGIN_SZ891   0.7949040  0.0533588    14.897  < 2e-16 ***
ORIGIN_SZ893   2.1604888  0.0490189    44.075  < 2e-16 ***
ORIGIN_SZ894  -0.1359986  0.0547355    -2.485 0.012968 *  
ORIGIN_SZ895   0.2839041  0.0559232     5.077 3.84e-07 ***
ORIGIN_SZ896  -1.0557229  0.0778987   -13.553  < 2e-16 ***
ORIGIN_SZ897  -1.5919544  0.0830914   -19.159  < 2e-16 ***
ORIGIN_SZ898   0.3561963  0.0636401     5.597 2.18e-08 ***
ORIGIN_SZ90    0.7284854  0.1126265     6.468 9.92e-11 ***
ORIGIN_SZ908   1.2975238  0.0554652    23.393  < 2e-16 ***
ORIGIN_SZ909   1.2758650  0.0496993    25.672  < 2e-16 ***
ORIGIN_SZ910  -1.5641346  0.0751951   -20.801  < 2e-16 ***
ORIGIN_SZ911   1.3884058  0.0501750    27.671  < 2e-16 ***
ORIGIN_SZ912   2.1014088  0.0491520    42.753  < 2e-16 ***
ORIGIN_SZ915   1.7913351  0.0492456    36.376  < 2e-16 ***
ORIGIN_SZ917   2.1560045  0.0497195    43.363  < 2e-16 ***
ORIGIN_SZ918  -0.7942207  0.0658344   -12.064  < 2e-16 ***
ORIGIN_SZ919   0.1503747  0.0552832     2.720 0.006527 ** 
ORIGIN_SZ928   0.5979938  0.0536540    11.145  < 2e-16 ***
ORIGIN_SZ929   1.5768886  0.0494344    31.899  < 2e-16 ***
ORIGIN_SZ930   2.7177274  0.0488340    55.652  < 2e-16 ***
ORIGIN_SZ931  -0.7799583  0.0641482   -12.159  < 2e-16 ***
ORIGIN_SZ932  -0.1604390  0.0645032    -2.487 0.012872 *  
ORIGIN_SZ933   1.6263276  0.0499933    32.531  < 2e-16 ***
ORIGIN_SZ934  -1.2538542  0.0670173   -18.709  < 2e-16 ***
ORIGIN_SZ935   3.4410215  0.0487029    70.653  < 2e-16 ***
ORIGIN_SZ938  -1.7911566  0.1890969    -9.472  < 2e-16 ***
ORIGIN_SZ939   3.1928261  0.0490494    65.094  < 2e-16 ***
ORIGIN_SZ940  -1.4060857  0.1316391   -10.681  < 2e-16 ***
ORIGIN_SZ949   0.7971592  0.0522774    15.249  < 2e-16 ***
ORIGIN_SZ950   2.7142670  0.0490885    55.293  < 2e-16 ***
ORIGIN_SZ951   3.1017847  0.0487891    63.575  < 2e-16 ***
ORIGIN_SZ952   0.0645352  0.0577960     1.117 0.264164    
ORIGIN_SZ953   0.9872612  0.0520900    18.953  < 2e-16 ***
ORIGIN_SZ954  -0.5576081  0.0587047    -9.499  < 2e-16 ***
ORIGIN_SZ955   2.0650230  0.0493686    41.829  < 2e-16 ***
ORIGIN_SZ956  -0.1801717  0.0537299    -3.353 0.000799 ***
ORIGIN_SZ957   1.8718853  0.0495067    37.811  < 2e-16 ***
ORIGIN_SZ959  -0.1511739  0.0839571    -1.801 0.071765 .  
ORIGIN_SZ961  -1.2293123  0.0661219   -18.592  < 2e-16 ***
ORIGIN_SZ962   5.7745401  0.0532620   108.418  < 2e-16 ***
ORIGIN_SZ970   1.1921473  0.0502249    23.736  < 2e-16 ***
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DESTIN_SZ86    0.7260597  0.1594095     4.555 5.25e-06 ***
DESTIN_SZ866   0.5768212  0.0714071     8.078 6.59e-16 ***
DESTIN_SZ867   0.7585897  0.0589746    12.863  < 2e-16 ***
DESTIN_SZ868   1.3572451  0.0567392    23.921  < 2e-16 ***
DESTIN_SZ869   2.1050638  0.0561623    37.482  < 2e-16 ***
DESTIN_SZ870   3.4177636  0.0537905    63.538  < 2e-16 ***
DESTIN_SZ871   3.1698544  0.0542345    58.447  < 2e-16 ***
DESTIN_SZ872   0.1475164  0.0589790     2.501 0.012378 *  
DESTIN_SZ873   1.4774013  0.0558912    26.434  < 2e-16 ***
DESTIN_SZ874   0.4132294  0.0577761     7.152 8.54e-13 ***
DESTIN_SZ875  -1.5636138  0.1709591    -9.146  < 2e-16 ***
DESTIN_SZ876  -1.2528896  0.1139698   -10.993  < 2e-16 ***
DESTIN_SZ877   0.8752557  0.0642626    13.620  < 2e-16 ***
DESTIN_SZ88   -0.3112785  0.0713029    -4.366 1.27e-05 ***
DESTIN_SZ887   0.9219216  0.0582036    15.840  < 2e-16 ***
DESTIN_SZ888   1.3215442  0.0559773    23.609  < 2e-16 ***
DESTIN_SZ889  -0.8870393  0.0856281   -10.359  < 2e-16 ***
DESTIN_SZ89    1.8004922  0.1132835    15.894  < 2e-16 ***
DESTIN_SZ890   2.4952869  0.0541577    46.074  < 2e-16 ***
DESTIN_SZ891   1.2207907  0.0580203    21.041  < 2e-16 ***
DESTIN_SZ893   2.3951509  0.0540602    44.305  < 2e-16 ***
DESTIN_SZ894   0.0420246  0.0601426     0.699 0.484708    
DESTIN_SZ895   0.2936932  0.0627834     4.678 2.90e-06 ***
DESTIN_SZ896  -0.9597254  0.0886007   -10.832  < 2e-16 ***
DESTIN_SZ897   0.0487346  0.0653942     0.745 0.456125    
DESTIN_SZ898  -0.0569965  0.0814203    -0.700 0.483910    
DESTIN_SZ90   -2.1701924  0.7099373    -3.057 0.002237 ** 
DESTIN_SZ908   1.4598512  0.0625797    23.328  < 2e-16 ***
DESTIN_SZ909   1.5559009  0.0548998    28.341  < 2e-16 ***
DESTIN_SZ910  -1.2344188  0.0790215   -15.621  < 2e-16 ***
DESTIN_SZ911   1.4853391  0.0555935    26.718  < 2e-16 ***
DESTIN_SZ912   2.2209778  0.0543258    40.883  < 2e-16 ***
DESTIN_SZ915   1.9973757  0.0543219    36.769  < 2e-16 ***
DESTIN_SZ917   2.0524858  0.0554613    37.008  < 2e-16 ***
DESTIN_SZ918  -2.0544832  0.1266824   -16.218  < 2e-16 ***
DESTIN_SZ919   0.1383903  0.0620486     2.230 0.025724 *  
DESTIN_SZ928   1.3816976  0.0572810    24.121  < 2e-16 ***
DESTIN_SZ929   2.0509963  0.0544464    37.670  < 2e-16 ***
DESTIN_SZ930   3.0004090  0.0539137    55.652  < 2e-16 ***
DESTIN_SZ931  -0.5236928  0.0716681    -7.307 2.73e-13 ***
DESTIN_SZ932  -0.0176144  0.0679217    -0.259 0.795377    
DESTIN_SZ933   1.7981745  0.0552843    32.526  < 2e-16 ***
DESTIN_SZ934  -0.9571716  0.0741014   -12.917  < 2e-16 ***
DESTIN_SZ935   3.9209491  0.0536928    73.026  < 2e-16 ***
DESTIN_SZ938  -3.1344144  0.3576496    -8.764  < 2e-16 ***
DESTIN_SZ939   3.6806950  0.0540076    68.151  < 2e-16 ***
DESTIN_SZ940  -2.5243172  0.1540211   -16.389  < 2e-16 ***
DESTIN_SZ949   1.3886428  0.0569564    24.381  < 2e-16 ***
DESTIN_SZ950   3.1172071  0.0541779    57.537  < 2e-16 ***
DESTIN_SZ951   3.8986546  0.0537552    72.526  < 2e-16 ***
DESTIN_SZ952  -0.3116557  0.0723433    -4.308 1.65e-05 ***
DESTIN_SZ953   1.2085404  0.0571902    21.132  < 2e-16 ***
DESTIN_SZ954  -0.1146922  0.0625693    -1.833 0.066796 .  
DESTIN_SZ955   2.7321405  0.0541824    50.425  < 2e-16 ***
DESTIN_SZ956   0.4496241  0.0576193     7.803 6.03e-15 ***
DESTIN_SZ957   2.2241828  0.0544058    40.881  < 2e-16 ***
DESTIN_SZ959  -0.8176268  0.1082431    -7.554 4.23e-14 ***
DESTIN_SZ961  -0.6731896  0.0737554    -9.127  < 2e-16 ***
DESTIN_SZ962   3.9554255  0.0541549    73.039  < 2e-16 ***
DESTIN_SZ970   1.6601328  0.0552779    30.032  < 2e-16 ***
DESTIN_SZ971   2.4047462  0.0541066    44.445  < 2e-16 ***
DESTIN_SZ972   2.2061362  0.0543502    40.591  < 2e-16 ***
DESTIN_SZ974   1.5897644  0.0556148    28.585  < 2e-16 ***
DESTIN_SZ975   0.8643165  0.0573796    15.063  < 2e-16 ***
DESTIN_SZ976   0.7481080  0.0576791    12.970  < 2e-16 ***
DESTIN_SZ977   2.1915623  0.0541778    40.451  < 2e-16 ***
DESTIN_SZ978   2.0489834  0.0552083    37.114  < 2e-16 ***
DESTIN_SZ982  -0.3602379  0.0629958    -5.718 1.08e-08 ***
DESTIN_SZ983   5.6957579  0.0579352    98.313  < 2e-16 ***
DESTIN_SZ984   3.7016773  0.0576697    64.188  < 2e-16 ***
DESTIN_SZ991   1.8631298  0.0555653    33.530  < 2e-16 ***
DESTIN_SZ992   2.0208901  0.0548401    36.851  < 2e-16 ***
DESTIN_SZ993   1.0246326  0.0558684    18.340  < 2e-16 ***
DESTIN_SZ994   1.2994702  0.0558729    23.258  < 2e-16 ***
DESTIN_SZ995   2.0152883  0.0547814    36.788  < 2e-16 ***
DESTIN_SZ996   1.2728739  0.0564216    22.560  < 2e-16 ***
DESTIN_SZ997   0.3874822  0.0677213     5.722 1.05e-08 ***
DESTIN_SZ998   2.7083900  0.0541109    50.053  < 2e-16 ***
DESTIN_SZ999   2.0389976  0.0548053    37.204  < 2e-16 ***
log(DIST)     -1.5622080  0.0004961 -3148.680  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 27137198  on 61827  degrees of freedom
Residual deviance:  5675541  on 60186  degrees of freedom
AIC: 5968031

Number of Fisher Scoring iterations: 10
CalcRSquared(dbcSIM_Poisson$data$TRIPS,
             dbcSIM_Poisson$fitted.values)
[1] 0.6682232

Conclusion of Doubly_Constrained model

Doubly_Constrained model demonstrates significant statistical strength, with all P-values being less than the 0.05 threshold, indicating a significant positive effect of the variables in the model on the predicted outcomes. The R-squared value of the model is 66.8%, suggesting that it accounts for a substantial portion of the variability in the response variable, indicating a good fit. Additionally, the model required 10 iterations of Fisher Scoring to converge, showing that the model underwent a reasonable number of iterations before reaching the optimal solution. Overall, the performance of this doubly constrained model is quite satisfactory. It effectively captures key features of the data, providing reliable predictions of the response variable. However, given that there is still room for improvement in the residual deviance, further exploration of additional explanatory variables or model adjustments might be needed to optimize performance and enhance explanatory power.

model_list <- list(
  Origin_Constrained = orcSIM_Poisson,
  Doubly_Constrained = dbcSIM_Poisson)
compare_performance(model_list,
                    metrics = "RMSE")
# Comparison of Model Performance Indices

Name               | Model |    RMSE
------------------------------------
Origin_Constrained |   glm | 392.509
Doubly_Constrained |   glm | 303.003

Modle Camparation Conclusion

The smaller the RMSE value, the smaller the error of the model. From the results, it can be seen that the Doubly Constrained Model (glm) has a smaller error compared to the Origin Constrained Model (glm). Consequently, in terms of performance, the Doubly Constrained Model (glm) is superior to the Origin Constrained Model (glm).

6,Visualization.

df <- as.data.frame(orcSIM_Poisson$fitted.values) %>%
  round(digits = 0)
inter_zonal_flow <- inter_zonal_flow %>%
  cbind(df) %>%
  rename(orcTRIPS = "orcSIM_Poisson$fitted.values")
df <- as.data.frame(dbcSIM_Poisson$fitted.values) %>%
  round(digits = 0)
inter_zonal_flow <- inter_zonal_flow %>%
  cbind(df) %>%
  rename(dbcTRIPS1 = "dbcSIM_Poisson$fitted.values")
orc_p <- ggplot(data = inter_zonal_flow,
                aes(x = orcTRIPS,
                    y = TRIPS)) +
  geom_point() +
  geom_smooth(method = lm) +
  coord_cartesian(xlim=c(0,150000),
                  ylim=c(0,150000))

dbc_p <- ggplot(data = inter_zonal_flow,
                aes(x = dbcTRIPS1,
                    y = TRIPS)) +
  geom_point() +
  geom_smooth(method = lm) +
  coord_cartesian(xlim=c(0,150000),
                  ylim=c(0,150000))
ggarrange(orc_p, dbc_p,
          ncol = 2,
          nrow = 1)
`geom_smooth()` using formula = 'y ~ x'
`geom_smooth()` using formula = 'y ~ x'

Conclusion of Visualization

The chart indicates that the Doubly_Constrained Model has a better fit than the Origin_Constrained Model, as evidenced by the smaller dispersion of points around the trend line, which suggests a lower error in the Doubly_Constrained Model compared to the Origin_Constrained Model.

7,Limitations

Limitations: 1,We have only compared two models; ideally, we could compare a wider range of models to select the most optimal one. 2,The data used were selectively chosen, which introduces the possibility of subjective bias in the dataset. 3,The model could benefit from a stepwise evaluation to determine if reducing the number of variables might increase the fit. 4,Due to memory limitations, ‘mapview’ cannot be used and the image lacks boundaries.